All mods depend on what your doing to the mower as far as if you are really going to race it or just pump it up and ride around the neighborhood.
The frame depends on the brand tractor you get and what class you plan on running. If your going in a class that requires big engines and a lot of torque, you may want to consider looking into the frame.
Usually any modifications to the speed of the tractor beyond stock require better brakes, usually a go cart brake setup is fine.
Your going to need a spring loaded throttle, not the rabbit, turtle lever throttle.
Yes there will be more strain on the clutch and belt.
I do wheelies on my lawnmower, you will want wheelie bars if you plan on doing wheelies.
Tranny, this is the tough one, I've already gone through one tranny, the gears are weak in most trannies, but there are a few desirable lawn mower trannies that do hold up.
This is a great forum for lawn mower racing.
http://www.heymow.com/