Dman979

Moved to Gameplay Questions and Tutorials.
 
Welcome aboard, @Mikenike! Most of my experience in the game has come from failing- a lot. I sincerely recommend trying to fail as much as you can. The harder it is to fail, the better you're getting at the game!
As for the specifics of your questions, I'll leave that to the other- smarter- forum members to answer.

Have you tried increasing the throttle? That's the first thing that comes to my mind, looking at your (very helpful!) picture.
Also, welcome aboard!

Hello, @Npreadr, and welcome aboard!
 
Yes, you can change the flag after you've started a game. If you want to change it for a specific ship, then when you're building look next to the name bar. You should see the current flag there. Click on it, and you should be presented with the full list of flags.
You can also change the save's flag. When looking at the KSC, before entering a building, click on the flagpole near the HQ. Again, you should see the same list of flags as when you started the game.
Hope this helps!

I've got good news and bad news for you, @Ncog Nito.
 
The good news is that you don't have to aim for the sun. The bad news is that you might need a very big ship.
 
In Kerbal Space Program, there is no way to escape the Sun's influence, short of being in a different SOI. As such, to get into a lower solar orbit from Kerbin, you just need to burn prograde on the early-morning side of the planet (the side facing forward with respect to Kerbin's orbit) until you reach escape velocity and leave Kerbin.
 
The bad news is that depending on the altitude the contract wants you to fly at, you'll need a lot of Delta-V. It costs about 1k Delta-V to escape from LKO, but that just gets you a little lower than Kerbin. In order to get even lower, you'll need to pack more DV, and more stages, into the ship.

Hmmm.
Can we get some pictures as to what your ship looks like?
Also, make sure that you haven't adjusted the trim on your ship. Press Alt+X and see if it helps.
Oh, and welcome aboard!

Your CNS looks fairly balanced around the vertical axis. My suggestion is to attach another docking port on top of the docking port. To that, add some fuel tanks, solar panels, a probe core, SAS, 2 radially mounted Monoprop tanks, RCS, and radially mounted engines. This thing will act as a kind of tug for your modules.
On the bottom of each module, add some folding landing legs. Space them so that when they deploy, they are linearly placed along the ventral side. Only one should touch the ground at a time. To form a tripod, use the wheels (set on brakes, of course).
After you land the first module, fly your tug back to munar orbit. Rendezvous with the next module, and dock. Fill the tanks with fuel, and burn to the surface. When you are almost at the ground, and moving slowly, deploy the legs. They should all stick out along the underside of the module. Land the module on a leg and two wheels. It should be vertical or almost vertical. To set it on the ground, close the first landing leg, and give a short sideways burst with the RCS. You should fall onto the second leg, and the next two wheels. Now might be a good time to remove that tug. Fly it away a safe distance, and land it.
Keep raising the gear until it's only the 4 wheels on the ground. Then drive the module over, and dock.
Also, Welcome Aboard!