"I like colored clothes" - Why not?
Because colored and colorful are not synonyms.
Colored is "pokolorowane"
Is "clothing" also correct?
"clothing" is more like "odzież", but it's fine and accepted.
Can "ubrania" ever be singular, or is it alway plural, like with "clothes?"
"ubranie" is one set of clothes: the ones you're wearing right now, the ones you will put on tomorrow, etc.