Survey: Do you have a fire extinguisher in the house? car?
It is impossible to sweat copper pipe with water in it. You will need to close the closest valve to shut off water where you are working. If the problem is due to a slow trickle of water even when the valve is closed, I have heard of wadding up bread crumbs (not the crust) into a ball and pushing it back into the water source side of the pipe. This will stop the water from interfering with your work and will dissolve once the water is turned back on. Hope this helps.
Compare it with a similar lock on another locker to see what the orientation is of the number plate. You may be able to find a good glue to repair it or perhaps you can try a double-stick style of tape. The tape can be applied in multiple layers if you need more thickness to fill a void. Put the tape on the back of the ring then trim away any excess before you secure the plate on the lock body. Good luck.
Single, well spaced, beeps are a detector warning you that the battery is running down. Just replace the battery (all of them if there is more than one) Even if they are hard-wired there ll still be a backup battery to replace.