mystifeid

The first requirement is not checked off - ie the station must be new, have a docking port, an antenna and can generate power. It looks like you have bulk solar panels and what looks like a few communotron 16 antennae but it's hard to identify docking ports in the image. One ship is clearly docked using a claw.
Also, did you dock older parts to the station before establishing orbit?

Welcome to the forums!
Alt + . on Windows  - that dot is the normal period (or full stop) key used for time warp, so just hold down Alt first.

Yes, you can use a rocket. You will see two notifications on-screen:
- "You are entering Sector P-PS" and
- "You are leaving Sector P-PS"
You must record the temperature in between these two events and you can be at any altitude below 17,700m. With a rocket you will be travelling reasonably quickly so have the thermometer window open, ready to click the button. Any rocket that you build that can reach that zone will be suitable. If at first you don't succeed you can always revert to launch and try again.
And, welcome to the forums!

And don't assign anything to the main throttle axis group. Use custom axis groups instead.
When testing for best speed it soon becomes apparent that there is a very narrow window for optimum prop pitch. You will either need to get lucky to find this optimum setting or have switched on fine control (caps-lock). Main throttle keys do not seem to respond to the use of fine control but custom axis group keys do respond.
As an example, if I takeoff and have rpm limit on the main throttle the smallest change I can make with or without fine control is 4 rpm with a sharp tap on the throttle keys. With rpm limit assigned to a custom axis group, the smallest change I can make with fine control switched on becomes on average 0.2 with the same sharp tap. With prop pitch on a custom axis group the smallest change I can make is 0.5 (or two taps to make a change of 1). Best speed is achieved within a prop pitch window of 0.5 - 1.
After takeoff, reducing prop pitch will usually increase speed until a point is reached where either the speed starts to drop or the current rpm (not the rpm limit) starts to drop below 460. The value of the prop pitch at this point is worth remembering. When starting a sharp turn or a steep climb it may often be worth changing the prop pitch back to this value. Effectively you can control airspeed and power by only using the prop pitch.
But you need the current rpm to drop in order to reduce prop pitch to achieve the fastest speeds.
If say, in level flight, the current rpm does not start to drop and speed reduces when you reduce prop pitch from this value, you can force it  by reducing the rpm limit and further reductions in prop pitch should see a marked increase in speed. At some point the current rpm will usually drop below the rpm limit. Quite often though, the current rpm will drop by itself leaving you to concentrate on finding the optimum pitch for speed.
When trying to find the best settings for maximum range, only two things seem to affect fuel consumption - rpm limit and torque limit. Again it will be a benefit to be using fine control with nothing assigned to the main throttle keys.
I find landing to be pretty easy. I reduce rpm limit and torque limit if for no other reason than making sure I don't run out of fuel before landing then on final approach, increase prop pitch back to 100 and drop the landing gear. Speed drops dramatically but flying in under power still provides good control.
All robotic engines can have an action group key assigned to toggle the motor direction. So on touchdown, reverse the engines until stopped or nearly stopped then use another action group key to toggle prop deployment. This is much safer and much more effective than using brakes.
Like @aegolius I disengage the engines in the SPH so my usual setup is something like this
Action group 1 - Toggle engage engines
Action group 2 - Toggle engine power (full torque on/off)
Action group 3 - Toggle prop deployment
Action group 5 - Toggle motor direction
Custom axis group 1 - prop authority
Custom axis group 2 - rpm limit
Custom axis group 4 - torque limit
So takeoff is as simple (after engaging SAS with the 't' key) as 1,2,3.
If you want to see a hard to land plane, you can check out the landing at the end of the video below which was made for the Kerboprop Speed Challenge - which requires a landing back on the runway. And it wasn't hard. The optimum prop pitch for speed with this plane is 29.5 - note that the current rpm is only 220.7 at 298.6m/s -  while the value for the prop pitch I use to maneuver is 70 and you can see me increase it back to 70 as I start the vertical climb preparatory to returning to the runway and then back to 100 just before landing.
 

Hi. I'm assuming you're using hinges. Have you tried assigning an action group key to toggle locking the hinges? Locking allows autostruts to pass through robotic parts. When unlocked, autostruts terminate at robotic parts. And when locked you might find you don't need autostruts.

Try using two inflatable heat shields - one on the top and one on the bottom. Also you could try reducing your orbit to something like 90-100km before deorbiting - ie so that your speed is down to around 3200m/s before starting your deorbit burn at the top of the atmosphere. If you have enough fuel and can decelerate to around 800m/s by the time you hit about 60km you can even ditch the heat shields altogether. But if you're going for the big aerobrake, they tend to flip and you'll probably need the two heat shields.
You can even get creative and try turning one of the heat shields upside down. Normally when you add an inflatable heat shield to a craft, it won't inflate - either in the VAB or in flight - if something is attached to the pointy end. But you can get around this by first using the rotation tool then the offset tool. (Be aware that if you then detach/reattach the heat shield it will no longer inflate and you will need to start over). You will also need to use the offset tool to attach another part to the other side of the heat shield. However, I'm not sure if this will make any difference to any propensity for flipping.
With two heat shields, possibly the thing that will have the most effect on stability is the distance between the heat shields.

Here's one for six thousand. A thumper and two hammers. Those AVR8 fins are expensive and you only need three. This one also includes a superfluous battery so you could take that out and make it a bit cheaper again. Still escapes Kerbin's SOI (with a decoupler). No steering required.

You need to lead the Mun a bit. Here's the current position (on the right) and the intercept position (on the left) of the Mun when the rocket above hits the top of the atmosphere . I'm missing it on the right so I could lead it by more and still get a fly-by.

Yeah, pretty sure It's the ring of six clipping ore tanks. When I duplicate that configuration in a much simpler vessel - like shown below - and cheat it into orbit, the same thing happens. Halfway through transferring the fifth tank I get an explosion. With certain things you can convince yourself that clipping them is not unrealistic but fuel/ore tanks sharing the same volume is not one of them and I'm not unhappy the game rejects it.
When I attach the ring of six tanks with tt-38k decouplers , a gap opens up between the tanks and I can then transfer ore into all six tanks with no explosions.

Actually I'm pretty sure it's because the fuel flow priorities have been set asymmetrically - ie tanks on one side are emptying before tanks on the other side are used.
Here are the fuel flow priorities for just the bottom six tanks. The ones on the left and right need to be the same, not different.

Kerbal Alarm Clock has a setting called "Halt timewarp when throttle cutoff by keystroke". Perhaps this is the problem.

1. I'm pretty sure it's by design.
2. Sometimes there might be three locations. Sometimes there might be as many as six.
3. Yes.
The contract usually includes something like "Vessel x has detected some temperature fluctuations to the north. Head in that direction and follow up with a series of reports."
(I think) It's impossible to tell when it will be finished until it's finished.