What's the exact meaning of this phrase: he isn' t a bad guy ( he's nice) or he doesn't feel bad?
He is nice, he is a nice guy or he is a good guy. It's has nothing to do with feelings.
He feels good or he doesn't feel bad.
I feel good or I don't feel bad
Is 'is not old' also correct?
Could this also mean ''my brother ain't bad'' It sounds a bit more colloqiul.
Sure, but as it's a regional expression so it seems logical to me that it isn't accepted here.