This should all be in the Q&A section, but to answer your questions:
No you cannot get the super rod without beating the E4 (you get it at the fight arena which is on the island with the battle tower and stark mountain).
When in the battle tower your pokemon above level 50 will be leveled down to level 50 temporarily to fight in the battle tower, they have the stats they would have had at level 50 with the current EVs, IVs and nature. They keep their current moveset. After the battle tower challenge is over, they return to their respective levels. Pokemon under level 50 do not get levelled up in the battle tower, so you have to use them on lower levels.