No you can not use Mewtwo or any other legenarie in the battle tower sorry.
you don't have to battle mewtwo first to get mew. you can battle either mew or mewtwo first.
Mewtwo is at Level 70 when you battle him. You should most likely use you highest level Pokemon that is around level 70.
There nowhere. After that all you have left to do is to catch mewtwo and that's it unless you want to do battle tower or something.
SnDGames
You can't get him with cheats, you have to battle him in an EX Raid Boss Battle, win, and ALSO hit Mewtwo with a Pokeball staying shut.
battle points known as BP are what you use for prizes at the battle tower.
No Exodia in a battle with mewtwo it´s a draw with arceus Exodia lose
you cannot ever beat the battle tower. but if you have completed the sinnoh pokedex then the battle tower will help you complete it. you can battle at the battle tower as long as you want.
You can either use R4 cheats or battle in battle tower.
Mo battle tower
after you get contunious battle wins at the battle tower
Your best bet is to use Mewtwo, he levels really fast early on, and can learn most of the TMs scattered about the dungeon.