Most of the Day Sailers were sold without an installed electrical system, some owners installed them aftermarket, me included. I originally had a Group-24 "dual-Purpose Battery in a box in hte cuddy just forward of the mast. I now have switched to a DC-1 size Deep-Cycle battery, and have it located just inside the cuddy on the starboard side. This balances the weight of my 4 hp outboard clamped to the transom, offset to port to clear the rudder. On a DS I you will need to install a platform to set the battery box on. I have a DS II and the box is secured to the molded liner of the cuddy.
Second answer, by "small compartment" in the stern, do you mean the "kickerpit"? that is the outboard mounting location, offset to port where the deck meets the transom (see pic below). If so, the YES, there originally was a cover included for that. Perhaps a fellow DS I owner could measure theirs? A piece of plywood, well sealed could be used to cover the kickerpit when the outboard isn't in place. I recommend sealing the plywood with epoxy or a good marine paint to reduce the chance of it swelling and getting stuck in place (would make mounting hte outboard more than a bit difficult!
As it turns out, it appears that the original factory-supplied covers were varnished marine plywood.