1. Damage counters always stay when you evolve unless there's a Poke Power/Poke Body that lets you. Special Conditions and all other effects are removed when you evolve, level up, go to the Bench, or go to the hand. Damage counters are also removed when the Pokemon card goes back to your hand.
2. Yeah, you can use any Basic Energy cards you want. In other words, they don't have to be Modified or DP-on. The exception is for the Special Energy Cards. Some of those are rotated out (Boost/DRE/Scramble)
dmaster out.