If you put some 4" perforated pipe behind the wall and back fill against the wall with crushed stone, it will pick up the runoff and not put a big load on your wall. You could then run the perforated pipe over to your sump pit that is going to pick up the water off your patio. I have seen large diameter pieces of plastic perforated pipe, 36" diameter, that can be used as your sump pit. Put your pump in the pit and then figure out where you are going to run your discharge. As for a cord, you should be able to use an out door cord that has 12 gauge wire. You might want to run the cord through a piece of conduit.