When looking at my fish, I cannot tell that some of my fish are currently breeding with neighbors fish.  They appear to be single.  There is no indication whatsoever that someone has accepted my breeding invitation.

They show as bred only when a friend has initiated breeding by sending me a breeding invite.  Shouldn't ALL of my bred fish (no matter who initated the breeding) have some kind of indication of being bred so I don't continually send out breeding invites?  If my fish has already been bred, what happens if I unknowingly try to breed it to a friend?  Will the initial breeding process be stopped?