Are my blood parrot cichlids breeding?

This is definitely breeding behavior. There are sites devoted to the Blood Parrot Cichlid (I have one too) and if you put in Blood Parrot Cichlid info on a Google search, you'll find the site. How big is the tank? That could be overcrowded. And the Blood Parrots are supposed to grow fairly large (6 inches or more possibly) and depending on the size of the tank, they will need more room. Their aggressiveness could be a sign of overcrowding as well. They are a cichlid so they are naturally territorial to begin with. Some are just naturally jerks and others are more aggressive only if they feel crowded. Unlike the other answer, Blood Parrots can have a , even though they are "man-made." They are bred from two different types of cichlids that normally would never meet in nature, that is why they are considered man-made instead of a natural mixed breed. There are Parrot Cichlids that do exist in nature and is typically one of the parents of a Blood Parrot, with the other parent being another type of cichlid although it is debatable which specific one it usually is. Blood Parrots have very big reactions to stress and if they are always fighting and are overcrowded, this could be very bad for you. Stress can cause Ick for everyone but for the Blood Parrot, specifically, it develops what is called Black Spot Disease. Blood Parrots do not naturally have any black on their bodies so if you see one with it, that is Black Spot. Trying to relieve a source of stress and giving them a good water change will help this. They can develop Black Spot if they are really stressed out or if the water levels are bad, some people even use them as a water indicator (don't suggest it) for that reason. Mine has gotten black spots every now and then, but I do a water change (usually 25 to 30%) and he clears up. It's not contagious to the other fish but if it's body is strained for too long, it will die. OH! And they can grow large supposedly, mine is still fairly young, but go to the Parrot Cichlid site because I believe it says they can grow to be at least six inches and live for over ten years. Best of luck to you and Big 'Un and Lil 'Un!!!!