Just to confirm - in a Rotation battle, the act of 'rotation' does take place before any move. I tested with Helping Hand, Feint, and Aqua Jet/Mach Punch; in all cases, the rotation occured first, followed by the move. Also, I believe that you don't take entry hazard damage when you rotate in a pokemon; however, if one of your three pokemon is knocked out, you send in another to replace it (well, you do in-game, at least) and in that case, you can take damage from entry hazards.
So, in effect, you can see a rotation battle as a triple battle in this regard; all of the pokemon who are 'rotating' are on the field, and don't take entry hazard damage from rotating; however, U-turning and so on is no different to a normal switch in that it incurs damage from entry hazards, as normal.
Edit: I just remembered that when I was testing Fire Burst, or whatever it's called, it did neutral damage to a fire type and a grass type (the overspill part of the effect, that is). I didn't test it on a flash fire user or another immunity, or on magic coat, however.