What I'm wondering is: Can I pickup Vcc and ground from pins 2 and 6 respectively of the 6-pin ISP header? Is there any reason I should avoid doing this?
Yes, you can, but I would not recommend soldering wires right into that location. It's a very nice thing to leave that port free just in case you want it at some point in the future-- either for reprogramming or as an SPI I/O port. If you want to use the power right from that location, it's better to first install the header there, and then to use a ribbon cable that connects to that location-- you can cut a ribbon cable cut in half, so that there's a connector on one end and loose wires on the other, too.
In any case, a better solution would probably be to use two of the free "Port C" pins, say
PC6 and PC7. Set one to high output, one to low output. They won't run at *exactly* 5 V and 0 V, but they'll be close enough to do what you need, and the pins are each rated for 40 mA, which is well in excess of what you'll need for an LDR.
Is PA7 my best bet for reading the analog voltage signal in?
Yes. The wiring to get there may be a bit cumbersome, but we left that analog line free specifically so that people could do this.
I might also point out that we normally use IR phototransistors for light sensing applications, since they ignore light from visible LEDs, but detect sunlight and incandescent room lights. But since you only need to respond to *very slow* changes, you should be OK with an LDR for this.
For physical mounting, you might consider putting the sensor on top of the case, with the leads going through the back ends of the ALARM button slots, or (if it's small) mounting it behind the red plastic, in the gap above the digits.