Now my home alarm panel is beeping. The backup battery needs to be replaced. It's some bizzarre kind of battery that I have to have the alarm company come and take care of. And of course it costs an arm and a leg!
The battery is usually attached by two small electrical connectors. Pull off the connectors, by grabbing the metal not the wire itself, either with your fingers or a needlenose pliars. Once you have the battery out it will be a simple matter of finding the model number and doing a search on it. It will cost you less than the alarm company will charge, plus they will probably hit you for a service call..unless its covered by some sort of maintenence agreement.
Regarding the outlet..you already took the covers off once, that's 1/3 of the job. Plug a radio in to the outlet, turn it up high and start cycling the circuit breakers off until the radio goes off. Then you know there's no power. At that point its a simple matter to either try to grab the broken off piece with, again, a pair of pointy pliars or get behind it with a small screwdriver. If you cant reach it, then a new outlet can be swapped out for about a buck. That doesnt require an electrician or any extensive wiring knowledge..just follow the existing layout of the wires.
Learn by doing. It's the best way.