some parrots can close their mouths, some can not. it doesn't really matter either way because even though they are hybrids, they are still cichlids. they have pharangeal jaws (a second set of chewing jaws further back in their mouths) which can nip long fins easily. in that case, having a mouth that closes just gets in the way.
while some people may have success with this mix, overall it is dependent upon the individual "personalities" of the fish as to whether they will fight or not. even putting juveniles together may work for a while, but as they grow and hormones cause them to become more aggressive and territorial they may fight, and behavior can change literally overnight.