5 - one at start, 1 for each tailor mission at lvl 20, 30, and 40, and 1 for Halloween event salvage - basically if it says unlock in game, you can do just that
Yes, they could have up to 5 more if they're willing to buy slots from the market...but then the account wouldn't be Free anymore...it would be Premium 
@Mistress Rue
Yes, I RP and play Redside on Virtue - No, Rumors of its demise have been greatly exaggerated
Do you suck at COH/COV? not yet...
Can a free to play player have more than one costume slot, and if so how many?