If I'm battling a friend in FireRed or LeafGreen at a Pokemon Centre, will our Pokemon be set to a certain level? Is it possible to do this also, like a option to set all Pokemon to level 50 or something along the lines of that? I do know this is a set thing in D/P on wards, but I wasn't sure about the Gen III games.
Nope. anything goes in LG/FR. The level you bring the Pokemon in is the level it is set to fight. So basically, it was to be the best and have the highest level possible before Gen IV. So no, there are no fancy features to set a Pokemon's level.
Source: I battle with my bro from time to time