torn fins can be from damage caused by transportation or other fish as well as "fin rot" (which looks like fin erosion) from stress or poor water conditions. I am dealing with this right now in some freshly caught naturals I am keeping. Make sure the tyank isn't overpopulated and water conditions are good. Adding a little salt may help.
tons of things can tear fins. getting snagged on sharp edges, fighting, agressive nipping etc. depending of the location and severity of the tear it should start to heal in a couple of days.