Slinky Strings- They may be a lighter gauge then your used to. If you put heavier strings on, you'll have to reset your trem, cause its a Floyed Rose.

Palm Mute- I wouldn't worry about your bridge moving by resting your hand on it. Your guitar has springs that help keep the tremolo system in place, so it shouldn't move that much.

Hands- I think its better not to rest your hand on anything, that way its free to move about faster, but whatever is more comfortable to you and more compatable with your playing style is probably best for you.