Build the rocket like normal.
After you are done, then hold down the SHIFT button, click on any part of the rocket. The entire rocket should now be "picked up" by your mouse cursor
Next, press the Q or E button. This will rotate your rocket.
For reference, the big open door in the VAB is due East (The direction you want to do your gravity turn towards). Rotate the rocket until it is oriented in that direction
Press " [ " or " ] " to switch active vessel. The vessel has to be close by (2.3km)
Antenna and relay connection follows the same rules as the initial craft, unless you want to use the "remote pilot" control (not necessary if you are in range of normal comms)
When you accept a contract (to put the first one into orbit), the contract is never attached to the probe. You see the probe/satellite as your one vehicle to complete this contract, but the game doesn't know that...it thinks that it is just some random attempt at a better comm network(even if it's on board parts completely satisfy the contract)
So the second contract just came about in the same way it usually comes about: there was a craft with some fuel on board in orbit, and this contract wants an adjustment. If you complete the adjustment first, you will get the money for the adjustment contract. The "place satellite" contract will remain, waiting to be finished. You can finish it with the same satellite(if you packed enough fuel), or you could send a new satellite that fulfills the contract.
An like @PT said, just ignore it if you don't want to do it, you won't get punished for not Accepting the "adjust orbit" contract
That will get you sorted. If you already know how to build a plane, then just follow those principles, but with MK3 parts
"...and my plane could not even go as high as 500m."
That sounds like patience, rather than wings or thrust. If it can fly, it should be able to reach up to 5 000m, given enough time though.
If you find it hard to go faster than 300m/s, then you might need more thrust(you shouldn't need more than 0.8 TWR on aircraft), or you need more altitude to break Mach 1
If you pitch you nose up to 15' but the prograde vector stays at 0'(meaning you are pointing upwards, but your altitude remains constant), then you need more wings.
"...I also had to hold the 'S' key to keep the nose up,..."
-Add more pitch control: any control surface for up/down movement on the tail will do...just go bigger?(You can also add them to the nose. CAUTION: Too much will make it "flip-happy")
-Or, move your wings around some. In the SPH, click the Center-of-mass button, also the Center-of-Lift button. What you are describing is called a "land-dart"...it does what arrows do. That happens when the yellow-ball is too far in front of the blue-ball.
> So move wings around until the blue-ball is only slightly behind the yellow-ball(the balls should touch).
> Right-click a fuel tank and empty it. This shows how the yellow-ball is moving around in flight as you deplete fuel...keep that in mind, because if the yellow-ball is BEHIND the blue-ball at any time in flight...you will be having a bad time ("flip-happy").
If you want to make cargo spaceplane, i suggest trying to build something similar to SKYLON. It does not even need to look like that, but it should function the same.
-Canards at the nose(like pitch elevators)
-High tail fin
-Elevons on wings(for roll)
With those basic components, things start handling pretty easy, even at re-entry speeds. I built one with the B9 mod part pack, and it is the most stable plane i have ever seen...re-entry at 60' pitch without my keyboard input, without any tendency to fall over/flip around.
It weights 59t at launch, and can put about 7t in LKO. It is not figher-like super maneuverable...rather it does slow and predictable movements, like a 747...at Mach 5
Blaarkies's post in Align parts in sky direction was marked as the answer