I'm really confused about battling... It seems entirely random what will happen no matter what ability I pick. 0.o Could someone explain the system to me please? 

Are you talking about PvP battles or PvE battles? EG battles under the "BATTLES" tab or battles on the islands?

Because, PvP battle pets follow their set auto-battle assignments. IE pets that have 5 stars in a certain attack are much more likely to use that attack than they are of an attack they have, say, 1 star in.

On the islands when you're facing random monstyers, however, it is completely random what attacks the opponents use. Because of this it is thought that it is better to simply use your strongest attack over and over. Since it's random there's no way to predict what strategy you should use, so you might as well hit them with your most damaging attack, right?