If I want to use a pokemon from Pokemon Crystal that's lvl

If I remember right, the opponent's levels scale based on your Pokemon's levels in Gym Leader Castle. In the leagues, your Pokemon need to be the right level.

No, all facility rulesets pre gen 4 scale up to your highest leveled mon if it doesn't have a hard level cap.

have fun grindin, op

Assuming you're talking about Ho-oH/Lugia. You're going to need to grind it up as well to use it in Stadium 2 as it will need stat.exp.

IIRC, it will have to kill each Pokemon in the E4 about 45 times to max it out unless you have Pokerus.