Gas car foams, usually rated just in shore, are a different type of foam from "carpet" tires. Also, they usually don't have the split compounds like a cyan (orange/magenta). On carpet, the carpet foams are usually faster.

As others have posted, tire size is usually based on the sidewall to reduce traction roll and help cornerspeed. Gearing may be easier, but the handling characteristics are most important in my opinion. 58mm would be pretty big for a race tire. Most are trying to be around 56.5 to 57mm. However, if you're not trying to win the nationals, it isn't really necessary to start the tires so small.

If your track is really grooved up, and the car is getting edgy, glue the sidewalls.
Otherwise, it's optional.

Parma, Jaco, CRC, BSR, TM all have the right compounds. Cyan and magenta, or dbl. pink/orange, dbl. pink in the case of Jaco and BSR?

The two stages seem to be good, esp. if your track is not super grooved up.

As far as sauce, do the whole rear and the front to taste, usually anywhere from 1/2 front to where the orange strip meets the magenta. Sauceing the whole front is usually a no-no, as it can make you flip.