Any level BF key should give you access to the BF, and unlock the dungeons up to its level.
If you click on the key and get a message that you have access to level X battlefields, then the icon should appear in the secondary skill list.
There should be one key for each dungeon, but if you miss a key, a higher level key will open the lower level dungeons as well.
The dungeons can be explored in any order once opened, but if you do the higher level dungeons first, you may not get as much experience in the lower level dungeons (ie if your character level becomes much higher than the monster level).
A couple people have run into problems leaving for the BF in the middle of a fight or cut scene and then returning, but there are no areas / spells that block access the BF, AFAIK.
The BF keys are always in the main game. Normal keys can be randomly generated in the BF, but they as useless and do not fit any locks.
In act 2, the level 6 key was in a cave to the far south east of the fire forest, reached by tossing a teleporter stone over some lava.