Some quetions I have before playing in icecrown

1- Is it possible to get Bis content without being a donor?

2- How long it takes?

3- Is there a difference between PvE and PvP gear?

4- Is there some kind of exp boost in icecrown?

I'm a complete noob, so I would appreciate your help.

1-Yes
2-Depends on how often you play, less than a year for full BiS is possible.
3-PvP gear has resilence stat which in essence reduces damage from other players. However, if you have too much PvP gear you won't do much damage so the trick is finding the golden middle.
4-Yes, XP is boosted by 7. So the XP rate is x7.

You just need a guild to get to a bis char. If you are in pugs, chances are that you will get 6k-6.1 max.

1. Yes
2. Depends on how active you are, and how skilled you are. If you are skilled and knowledgeable you can join an LOD guild and get BIS a lot faster, if you know nothing you will take some time in pugs learning the fights or can join a learning guild (they do exist). I have a rshaman who dinged 80 less than 2 months ago and is 6.3k just because I'm a core raider in an LOD guild (still missing 7 BIS items out of 17, but the 7 items are pre bis more or less). I would say 6 months is reasonable if you are in LOD guild and not donating and decently active. Without donating you will never be BIS without being in an LOD guild and knowing tactics.
3. PVP gear has resilience as a stat, don't use that crap in PVE content.
4. Icecrown is 7X exp rate, if you are familiar with the game you can reach max level in a day or two.