Alarm Circuit

I am attempting to design a circuit that is battery backed-up and will sound an alarm if the switch in the schematic is opened.

1) Is the attached circuit functional?

2) Am I using an appropriate voltage regulator?

3) Is the capacitor necessary for the circuit? If so, what is the least amount of capacitance required?

What kind of battery are you going to use?
That is the most critical design requirement of you supply.
You need to properly charge your battery or it will not last.

Your current design does not allow for proper charging of the battery (as 4pyros alluded to).

For proper charging, the battery needs a charging level greater than its rated 12VDC nominal output (ideally, 13VDC or greater). And the charging current needs to be controlled as well to avoid over-charging (think "trickle charge").

The 12VDC regulator output, minus the diode and 100ohm resistor voltage drops, will only provide <12VDC for charging purposes.

Strictly for fire safety reasons, I would not put anything in the attic but the siren. I would have the battery totally isolated from your circuit by a relay (wired such to provide battery power on loss of mains) and charged by a separate trickle charger and the entire system (except for the siren) anywhere but the attic.

After viewing some different "trickle charge" schematics, I have decided to explore the possibility of using a non-rechargeable battery as a back-up (Energizer A23). Would the attached schematic work?