Cpt Kerbalkrunch

Do you have advanced tweakables enabled? Haven't checked, but I don't think the overlay was removed.

Agreed. Use Tylo for the free capture (Laythe works as well, but since you're going to Pol, probably better to stay further out). Once you see that you have a projected orbit, you have all the time in the world (about a year and a half) to mess around with maneuver nodes to line up the best Pol encounter you can. Either burning in the SOI of Jool or Tylo itself should get the job done for pretty cheap. And Pol's gravity is so low, the land and return to Kerbin can be done with a very small lander. Even a larger one is pretty straight forward if you wanna bring along some extra Kerbals to gain experience. And since this is a career game, it wouldn't hurt to send a detachable probe with a survey scanner to scan Pol for ore. It's a pretty good insurance move for future exploration. Pol is a great place to set up mining operations to refuel Jool missions.

It's because you don't have a Commnet connection with the KSC. Your resource window isn't open, so I can't say if it's because you don't have power or just because your antenna is unable to reach Kerbin. If this is an old game, disable Commnet in the Settings menu. Otherwise, you're gonna need to set up some relay antennas.

Honestly, once you can, it would probably be best to have one on each of the moons (if only just for fun and the challenge of it). I even have a very small one on Tylo. That one is only useful for Tylo landers, though. Not refueling operations. Laythe is the same way. It would almost be like having refueling operations on Kerbin (which people certainly do). It's entirely doable if you're good with spaceplanes (which I'm not), but it would really only be useful at Laythe. However, it costs so much to operate around there (as @Spricigo mentioned) that it might be worth it if you end up spending a lot of time there.
As @bigcalm said earlier, Vall is in a great spot, but it costs more to operate there. It leaves a choice a lot like at Kerbin. Kerbin itself (Laythe), Mun (Vall), or Minmus (Pol, Bop). With those choices, Pol, I really think, is the best option for your first base at Jool. You can launch a huge fuel shuttle off of Pol easily, and use it anywhere in the system. Even if it only has a little fuel left to transfer (subtracting what it needs to take off, get where it's going, and then get back), it still does the trick. When you're returning to Kerbin, you usually don't have much of a ship left. This means you don't need a lot of fuel, you just need a quick fill-up to get home. Combined with the free-capture at Jool, you can make your ships quite a bit smaller, and even make them "one-way" so-to-speak, since they can refuel before heading home. If your ship has some fuel left (but not enough to get back to Kerbin), you can have it stop off at Pol on the way home to refuel. It also really provides a great safety net for your early Jool operations; when you're not too sure what you're going to need. I highly recommend beginning at Pol.
You'll notice in my pic above that I also have an operation on Bop. It was built to complete contracts, of course, but also because I take a lot of contracts at Bop even now. The money is always good, but mostly because I just like Bop. I wouldn't recommend it for your main operation, not just because of the inclination (as Bigcalm also mentioned), but because landings there happen in slow motion (a lot like Gilly) and can be infuriating if you're in a hurry.

Welcome to the forums!
Tough spot, but not insurmountable. You need a rescue mission, obviously, but you have several options. Either send a ship out to rendezvous and EVA your Kerbals over to the rescue vessel or, if you have the Klaw unlocked, you can grab the ship and tow it home.
Alternatively, your Kerbals can aid in their own rescue. It shouldn't take much to intercept Kerbin, of you wait for the right time, and your Kerbals each have 300m/s worth of monopropellent in their tanks. That should let you get an encounter with Kerbin, where it'll be easier to scoop them up. However, since there are three of them, it might be a little bit trickier. But still doable.
Whichever method you choose, you can bring your Kerbals home. So don't give up. Best of luck.

Have you already reached Jool? The reason I ask is that, if you catch Tylo (or Laythe as well) on the backside of Jool (when the moon is on the retrograde side of Jool's orbit around the sun), you will capture without any burn at all. This is one of the best things about going to Jool. You can plan for this in your design, and take advantage of the savings. Your ship is already built, obviously, but it looks just fine to me. I don't use the Nerv, so I'm not as familiar with it, but I think I'd forget about Laythe. The cost isn't worth it. I'd just run experiments and EVA on the way through. After passing through, you can also easily get a rendezvous with Vall and Tylo for flyby science grabbing (they're actually tough to avoid). 
To me, Pol or Bop should be your goal. With what you have for your lander, you could mine either moon for all the science it has. You should be able to return to Kerbin with your first Jool mission a resounding success. And when you do, I'd forget the aerobrake. If your ship isn't designed for it, you'll have to stay so high that the result will be small and not worth the risk. Remember that you'll be doing the Jool-dive, and moving extremely fast. Easily doable with a shield, but most likely disastrous without one.

@Chads Not to be glib, but your interplanetary ships can be as large or small as you want. It simply depends on what you intend to do when you get there. Are you going unmanned, or sending Kerbals? That will dictate what size ship you need, for the most part. For my first forays beyond Kerbin, I sent four ships at roughly the same time (which I thought was a lot back then). Two ships went to Duna/Ike and the others went to Eve/Gilly. The first ship of each pair was a probe with a survey scanner (and all the other science equipment I had), and the second was a manned ship with 2 Kerbals (a pilot and an engineer) and drills/converter. Each probe went to its planet and scanned for ore, then went to its moon and did the same.
Since I was completely inexperienced, and had no idea what to expect, I felt that this approach would give me maximum flexibility and a good safety net. Each ship would land on its planet, mine for ore and refuel, then head to its moon and do the same before going home. Your already on the forum, so you probably know more than I did at that point. In which case, you can probably guess that I went 3 for 4. The Eve mission was a spectacular failure. Or perhaps a "successful failure". I learned a lot, and since I just reloaded and went to Gilly instead, I probably saved myself a huge hassle because, knowing what I know now, the ship never would've left the surface anyway.
Anyway, after launching the 4 vessels, I was so broke I couldn't afford to launch another. I had to timewarp ahead and complete the missions. I had taken about half a dozen contracts, and all of them cashed in (except plant flag on Eve; took another decade before I tried again). The money I got from those contracts (not to mention the ton of science) propelled my entire space program, and I've never looked back. So, I wouldn't sweat the cash. Just accept the contracts and bring what you need to fulfill them. And if you can grab more doable contracts on the way, grab 'em. Afterward you'll see, interplanetary contracts are so lucrative that they pay for themselves with some cash left over. And if you stack contracts, you'll have a lot left over. Soon you'll be swimming in cash and won't need to worry about it at all.
So, my recommendation? Send some Kerbals. It's always more fun, I think. And the experience (for you and your Kerbals) is invaluable. Hope all goes well.

I've definitely wanted to do that before as well. Unfortunately, it's usually after I've launched that I realize I wanna be able to turn certain thrusters on or off. At that point, you can only do it the hard way and disable one thrusters at a time manually. If you haven't launched yet, you can make an action group to quickly turn them on and off. Still not the same as disabling crossfeed, but it'll at least give you the control your looking for.

As @DrLicor said, the root part is what matters. Use the root tool in the VAB to make the docking port on the launch vehicle the root part. Do the same with the payload. Now when you merge them, they'll connect together easily.