Leganeski

Moho and Gilly both have significantly eccentric orbits, making a straight Hohmann transfer impossible. The best route I know of involves dropping down to Eve and putting your periapsis at the right longitude so that when you eject from there to Moho, the transfer meets Moho at periapsis. It requires an awkward ejection from Gilly, but saves a lot of fuel at Moho.
Gilly to Eve: 180 - 680 m/s depending on Gilly's location Eve to Moho: 640 - 730 m/s Capture / ejection at Moho: 1020 - 1060 m/s Landing / takeoff at Moho: 850 - 870 m/s This adds up to a total cost of 2700 - 3350 m/s in each direction. That isn't enough to require a specialized ion vehicle, especially not if you have ISRU, but Moho's moderate gravity (0.275 g) can be challenging for motherships to land on.
The route I took to Moho in my grand tour mission actually went Minmus-Moho-Mun so that I could use the full gravity assist potential of Eve in both directions. (Technically, it was Moho from stock-scale JNSQ, but it has a very similar size and orbit as stock Moho, and that entire section of the mission would have worked almost identically in the stock system.) I packed 8800 m/s of delta-v because I didn't want to worry, but I only ended up using 4360 m/s to get from Minmus to Moho, and that was with a terrible Moho encounter. With a better placed Eve assist, it could have taken less than 3200 m/s, and the theoretical minimum for that route (in the stock system) is about 2320 m/s.
In summary, getting the mothership to Moho and back is totally doable, but will likely require some careful orbital maneuvering.

Your propeller blades are arranged asymmetrically: they are deployed in the same direction, but the motors are spinning in opposite directions, so one set of blades is producing backwards thrust.
Try setting the variant of the propeller blades on the one of the engines to "counterclockwise". (I don't remember which one it should be; try both separately and see which one makes the plane go forwards.)

This is because you landed so far away from the equator. Thankfully, when coming back from Mun, there's a relatively simple solution to the problem of inclination.
After reaching low Mun orbit, create a 290 m/s prograde maneuver, and move it around until the planned trajectory exits Mun's sphere of influence horizontally. (The maneuver should be positioned about 45 degrees after your orbit crosses the equator.) This gets rid of the inclination by using Mun's gravity to rotate your velocity towards the direction you want. Click the "next orbit" button repeatedly until the planned trajectory reaches Kerbin. (This could take up to 60 orbits, depending on where Mun is.) Execute the maneuver.

This is probably the most important part. Because Laythe orbits so quickly, it's really important to meet it in exactly the same direction as it is moving around Jool, effectively allowing you to subtract off Laythe's full orbital velocity (3223 m/s) from your velocity around Jool. As it is, you're meeting Laythe about 60 degrees too early, which is always going to waste at least 1500 - 2000 m/s.
Thankfully, the Laythe encounter problem isn't too hard to fix: you can make a correction maneuver halfway along the route to Jool which moves the entire Jool flyby about an additional two hours into the future. Keep adjusting it until the planned trajectory encounters Laythe just as it is about to reach its closest approach to Jool. This will save a lot of fuel when you reach Laythe, and 2800 m/s should probably be enough to complete the capture.
 
As others have stated, another relevant thing to get right is the transfer to Jool. Although your transfer isn't terrible, and is likely good enough considering how much extra fuel you packed, encountering Jool in the same direction that it is moving will save even more fuel. If you line up both encounters well, it costs less than 500 m/s to capture at Laythe.

This is probably the most important part. Because Laythe orbits so quickly, it's really important to meet it in exactly the same direction as it is moving around Jool, effectively allowing you to subtract off Laythe's full orbital velocity (3223 m/s) from your velocity around Jool. As it is, you're meeting Laythe about 60 degrees too early, which is always going to waste at least 1500 - 2000 m/s.
Thankfully, the Laythe encounter problem isn't too hard to fix: you can make a correction maneuver halfway along the route to Jool which moves the entire Jool flyby about an additional two hours into the future. Keep adjusting it until the planned trajectory encounters Laythe just as it is about to reach its closest approach to Jool. This will save a lot of fuel when you reach Laythe, and 2800 m/s should probably be enough to complete the capture.
 
As others have stated, another relevant thing to get right is the transfer to Jool. Although your transfer isn't terrible, and is likely good enough considering how much extra fuel you packed, encountering Jool in the same direction that it is moving will save even more fuel. If you line up both encounters well, it costs less than 500 m/s to capture at Laythe.

This is probably the most important part. Because Laythe orbits so quickly, it's really important to meet it in exactly the same direction as it is moving around Jool, effectively allowing you to subtract off Laythe's full orbital velocity (3223 m/s) from your velocity around Jool. As it is, you're meeting Laythe about 60 degrees too early, which is always going to waste at least 1500 - 2000 m/s.
Thankfully, the Laythe encounter problem isn't too hard to fix: you can make a correction maneuver halfway along the route to Jool which moves the entire Jool flyby about an additional two hours into the future. Keep adjusting it until the planned trajectory encounters Laythe just as it is about to reach its closest approach to Jool. This will save a lot of fuel when you reach Laythe, and 2800 m/s should probably be enough to complete the capture.
 
As others have stated, another relevant thing to get right is the transfer to Jool. Although your transfer isn't terrible, and is likely good enough considering how much extra fuel you packed, encountering Jool in the same direction that it is moving will save even more fuel. If you line up both encounters well, it costs less than 500 m/s to capture at Laythe.

This is probably the most important part. Because Laythe orbits so quickly, it's really important to meet it in exactly the same direction as it is moving around Jool, effectively allowing you to subtract off Laythe's full orbital velocity (3223 m/s) from your velocity around Jool. As it is, you're meeting Laythe about 60 degrees too early, which is always going to waste at least 1500 - 2000 m/s.
Thankfully, the Laythe encounter problem isn't too hard to fix: you can make a correction maneuver halfway along the route to Jool which moves the entire Jool flyby about an additional two hours into the future. Keep adjusting it until the planned trajectory encounters Laythe just as it is about to reach its closest approach to Jool. This will save a lot of fuel when you reach Laythe, and 2800 m/s should probably be enough to complete the capture.
 
As others have stated, another relevant thing to get right is the transfer to Jool. Although your transfer isn't terrible, and is likely good enough considering how much extra fuel you packed, encountering Jool in the same direction that it is moving will save even more fuel. If you line up both encounters well, it costs less than 500 m/s to capture at Laythe.

Did you set the navball to orbit mode? If you don't, it will calculate prograde as surface prograde, which doesn't deviate from vertical until after you start turning.

Without any gravity assists, the cheapest route is a direct transfer from Kerbin to Vall and back.
After reaching LKO, the ejection to Jool costs 1920 m/s, and the injection at Vall costs 980 m/s, for a total of 2900 m/s. After landing and rejoining the mothership, the ejection back to Kerbin costs another 980 m/s.
If you have a more capable lander, you could theoretically save 260 m/s in each direction by parking the mothership in an elliptical Vall orbit, which would reduce the total Δv requirement of the mothership from 3880 m/s to 3360 m/s.

The Panther in wet mode has an Isp of 4000 s. The exact fuel consumption depends on how long you use the plane for, but I'll take a wild guess and say you might need an average TWR of 0.4 for an hour. In that case, your plane would to be about 30% fuel by mass.
That's a lot, but in practice, you wouldn't be using wet mode the whole time, which would raise the efficiency a lot, and a fighter jet might not need to be constantly executing maneuvers for an hour straight. If I made a fighter jet, I'd probably stick with dry mode the whole time (Isp: 9000 s), and run it for like twenty minutes before landing back down. Then the plane would only need to be 5% fuel.
(Note that the number of engines doesn't matter other than letting you fly the plane at a higher TWR if you want.)

This is the only problem that I could see.
Because the center of lift is so far back, it's constantly trying to tilt the plane downwards. On the ground, this means that the front wheel is supporting most of the weight of the plane, and one wheel isn't enough to maintain stability. In the air, your control surfaces are fighting as hard as they can to counteract the downwards tilt, and are just barely succeeding. When you use them to do something else like turning, they can no longer provide enough pitch torque, and the plane pitches downwards and crashes.
Still, the fact that you managed to actually achieve level flight after only 10 hours is very impressive! It took me a lot longer than that.

I'm not sure how exactly FAR works, but this is probably because you're flying really fast through dense air. The dynamic pressure on your plane at the time of the screenshot is about 132 kPa (assuming you're at the equator just before noon, which is what it looks like to me based on Kerbol's reflection in the water). In comparison, a typical rocket launch in real life reaches a maximum dynamic pressure of about 30 kPa, and even that's enough to cause significant structural concerns.
When you're flying against that much pressure, slight pitch adjustments will cause the wings to start producing a huge amount of lift, and in this case, it's more than they can handle.
There's a reason why planes don't normally go supersonic until they're high up in the atmosphere.

In general, it is possible to use multiple planet packs simultaneously: just install both of them. However, it is possible for two planet packs to have planets that occupy the same space, in which case those particular packs will not be compatible with each other.
If you're using Kcalbeloh as a secondary system, it is quite far away, at a distance of 251 - 292 Tm away from the central star. No other planet pack that I know of occupies that range of distances, so anything should work fine with it.
If you're using Kcalbeloh with the homeswitch, you can still add other planet packs as long as they don't also move the homeworld (i.e. GEP or OPM should work, but not Beyond Home). They will orbit Kerbol as usual.
If you're using Kcalbeloh as a primary system, where Kcalbeloh takes the position of Kerbol, planet packs such as OPM that expect the stock system will not work. Other packs may work as long as all the systems they add stay far enough away from Kcalbeloh to avoid overlapping SOIs. Aralc's SOI extends to a maximum of 1.4879 Tm away from Kcalbeloh, so anything farther away than that should be compatible. For example, GPP Secondary (3.304 - 10.696 Tm) would work, while GEP (0.7 - 3.3 Tm) gets too close.

In general, it is possible to use multiple planet packs simultaneously: just install both of them. However, it is possible for two planet packs to have planets that occupy the same space, in which case those particular packs will not be compatible with each other.
If you're using Kcalbeloh as a secondary system, it is quite far away, at a distance of 251 - 292 Tm away from the central star. No other planet pack that I know of occupies that range of distances, so anything should work fine with it.
If you're using Kcalbeloh with the homeswitch, you can still add other planet packs as long as they don't also move the homeworld (i.e. GEP or OPM should work, but not Beyond Home). They will orbit Kerbol as usual.
If you're using Kcalbeloh as a primary system, where Kcalbeloh takes the position of Kerbol, planet packs such as OPM that expect the stock system will not work. Other packs may work as long as all the systems they add stay far enough away from Kcalbeloh to avoid overlapping SOIs. Aralc's SOI extends to a maximum of 1.4879 Tm away from Kcalbeloh, so anything farther away than that should be compatible. For example, GPP Secondary (3.304 - 10.696 Tm) would work, while GEP (0.7 - 3.3 Tm) gets too close.

In general, it is possible to use multiple planet packs simultaneously: just install both of them. However, it is possible for two planet packs to have planets that occupy the same space, in which case those particular packs will not be compatible with each other.
If you're using Kcalbeloh as a secondary system, it is quite far away, at a distance of 251 - 292 Tm away from the central star. No other planet pack that I know of occupies that range of distances, so anything should work fine with it.
If you're using Kcalbeloh with the homeswitch, you can still add other planet packs as long as they don't also move the homeworld (i.e. GEP or OPM should work, but not Beyond Home). They will orbit Kerbol as usual.
If you're using Kcalbeloh as a primary system, where Kcalbeloh takes the position of Kerbol, planet packs such as OPM that expect the stock system will not work. Other packs may work as long as all the systems they add stay far enough away from Kcalbeloh to avoid overlapping SOIs. Aralc's SOI extends to a maximum of 1.4879 Tm away from Kcalbeloh, so anything farther away than that should be compatible. For example, GPP Secondary (3.304 - 10.696 Tm) would work, while GEP (0.7 - 3.3 Tm) gets too close.