you go to the main campaign and it should give you the option of changing your suit. (assuming you have the suits downloaded)
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There is a Batman Beyond suit, a 1970's Batman, Batman Inc., Year one Batman, Earth One Batman, Batman The animated series (TAS), Sinestro Corps Batman, And The Dark Knight Returns Batman
The only alternate suit I have seen is the Armored version, unlockable after beating the games story mode. Sadly, it is only for Challenge mode.
you need to find the red brick for it.
The armor plating makes the demolition suit bullet proof.
Character Studs are like coins. They buy characters, extras, suit upgrades, etc.