1) The driver station (the program which communicates between your computer and the robot) runs on LabVIEW, so unfortunately your required to download it.
1) The link above is exactly what you need.
2) Nope. In fact, I would strongly recommend that you try to find a different computer to program on.
3) I would suggest
this, especially if you plan to eventually add something extra to your robot besides the drivetrain.
Also, calm down. You have 3 weeks. There is no reason that you shouldn't manage to get the robot programmed by then, considering you already have it built and wired. And if you don't, there will be about 100 smart, friendly people willing to help you get it functioning at your competition.
Good luck!