"I also see some people mention auto-takeoff"
It's enabled by default. It's under the "flight section" of the clip board.
When you are in the tower, click one of the north or south square, not the "H" for hanger.
Then as your plane starts to roll, don't touch it. With auto take off enabled, you should be getting into the air completly "hands off".
"Activating autopilot does nothing"
It won't, on the ground. It all works once you're up, and is a subject in it's own right, as is trim.
"I can take off basically, but right after takeoff the aircraft gets pulled to the side and if I try to correct it, it goes into a spin and crashes"
Basicaly, you're not fast enough. If you insist on taking over at take off, keep the nose low, get the wheels up as fast as possible and do nothing until you can see 200 mph. Then, very gently, start to make control inputs. With practise, you can be off and manouvering under 200, but almost all of the frustrations of a beginner are simply the result of not being fast enough for the manouver you're trying to perform.
For your first flights, pick an airfield that's go no mountains or obstructions around it.
Click one of the compass buttons on the clipboard, don't try driving from the hanger, it disables auto take off (control input).
Use auto take off. Resist the urge to take over. Sit back and let it climb a couple of thousand feet. Then push the nose forward to gain speed to about 200-250, and you're away.
Once you can reliably get up in the air, you can start making it harder for your self
