I can BG pretty well, but I am mostly a defensive person and I can't BG on my clothies, they just get ganked. I have a mixed group with a healer, Draeneis GotN (DKs and hunters) and 4 locks+priest. 90% of my healing is:
/cast [target=focus-target-target] HealSpell

I map it to one key and use it like crazy. I start off with:
/castsequence [target=focus-target-target] reset=15/target Renew, Flash Heal, Flash Heal, Greater Heal (sub in different class spells)
It lets me start off small, and work my way up.
I add in:
/castsequence [target=focus-target, help] {reset of stuff}
before hand so I can heal anyone in case of emergencies (out of group people). Just have to put it first so it gets done first.

I also have a spam heal spell that I use for just heal like crazy. It changes with levels. Lower levels it is (from priest point of view), bubble (since it is instant and it gives me time to cast), flash heal (since it is smaller and maybe person just needs topped off), and greater heal. Pretty much same as normal one, just tougher and won't work on out of group people (since can only bubble in group/raid). As I move up, I add in funner spells, like Prayer of Mending and such.

I don't think I would ever, PVP without playing the healer as my main. I can attack stuff without paying attention, but my healer (softie) would get ganked so much that I would just be donating a free HK to them. Plus attackers have a few moves, but for me, healers have WAY too many moves to either map keys to or macros that would fit the situation. Sorry I can't help much other than general stuff. I could never, ever do arena.