Colo links up with R/S/E & FR/LG. In other words, it can link up with all of the 3rd Generation games. I'm not sure about Emerald though. Never tried.
In Battle Mode, I think those are the only kinds of battles, it's been awhile since I played Colo so I can't really remember. I'll go check.
Edit: Yep, only Lv. 50 and Lv. 100 Battles, but your Pokemon can have any level they like as long as it doesn't go past the restriction. But it'll benefit you if you have Pokemon at the matching levels depending on which one Colosseum enter. However, with Mt. Battle they match the level of your strongest Pokemon just as long as they're past Lv. 50.
eg. Your team consists of:
Jolteon Lv. 86
Charizard Lv. 79
Ludicolo Lv. 84
Your opponent's Pokemon will all be Lv. 86, but your Pokemon's levels will stay the same.
All this is just for Battle Mode.