1) All frames can resonate, but steel is abetter choice.
2) I'd use 2010 ballscrews.
3) Do you mean round shaft when you say linear bearing? Accuracy will be the same for both.
Hiwin or THK type profile bearings are much stiffer and stronger, and can provide better quality cuts.
4) If you'll be running at 20,000 rpm for long periods of time, then water cooled may be a better choice. But air cooled are much simpler, and work fine. They are louder, though.
5) It depends on the drive system you are using.
I would not buy either of those kits.
Motors should be the last thing you choose, after the design is complete, and you know all the components that you'll be using.
6) two motors.
7) belt reduction, but a single belt is usually not enough reduction. Worm gears will typically have too much backlash. Again, motor choice depends on exactly what components you're using, and the performance that you want to achieve.