I can help answer #4, #5, and #6 for you.
For coding mecanum wheels, the first thing to do is to make sure that they are put on correctly. The direction of the “spikes” of the wheels should be making an X. To move in the direction you want, you spin the wheels in the direction you want to go and on the other side, you spin them out. Here’s some sample code that used buttons and joysticks and here’s a visual from a while ago:
if(vexRT[Btn8U] == 1){
setMultipleMotors(speed, frontRight, backRight, frontLeft, backLeft);
}
else if(vexRT[Btn8D] == 1){
setMultipleMotors(-speed, frontRight, backRight, frontLeft, backLeft);
}
else if(vexRT[Btn8L] == 1){
setMultipleMotors(speed, frontRight, backLeft);
setMultipleMotors(-speed, frontLeft, backRight);
}
else if(vexRT[Btn8R] == 1){
setMultipleMotors(-speed, frontRight, backLeft);
setMultipleMotors(speed, frontLeft, backRight);
}
else if(vexRT[Btn7L] == 1){
setMultipleMotors(speed, frontRight, backRight);
setMultipleMotors(-speed, frontLeft, backLeft);
}
else if(vexRT[Btn7R] == 1){
setMultipleMotors(-speed, frontRight, backRight);
setMultipleMotors(speed, frontLeft, backLeft);
}
else{
motor[frontRight] = vexRT[Ch3] - vexRT[Ch1] - vexRT[Ch4];
motor[backRight] = vexRT[Ch3] - vexRT[Ch1] + vexRT[Ch4];
motor[frontLeft] = vexRT[Ch3] + vexRT[Ch1] + vexRT[Ch4];
motor[backLeft] = vexRT[Ch3] + vexRT[Ch1] - vexRT[Ch4];
}

I’ve never used an autonomous selector myself. What I’ve done is just upload programs to different slots and rename them after I got the right auton selected. I did this by using defines and #ifdef statements in my code to get the correct one. But if you have time for one, go for it, just don’t make it your first priority.
As to what API you should use. I prefer PROS because I think it’s simpler to code in. The API has more features than VEXcode I think. The way it’s structured makes much more sense. It also has great command line tools if you want to use your own editor, or you can use the one it comes with. VEXcode is not finished in my opinion and lacks many features.