Yes, regearding the switching of peripherals, i am talking specifically about the off-board hardware peripherals, the camera and the pyro sensor in particular.
You could try connecting the +ve pin of the pyro sensor to 'Pi +ve 'via the C-E pins of an PNP tranistor. The base of that transistor could be connected to the Pi's GPIO so that when you want the pyro sensor to be active just turn the transistor on to connect the pyro's supply to the Pi's supply. When the transistor is off the pyro sensor would be drawing no current. It doesn't look like a power hungry module but sometimes every little helps.
The camera module is another possibility. Talking off the top of my head here because I haven't so much as glanced at the camera datasheet yet, but if there is nothing in the Pi's config files to allow you to kill power to the camera when it isn't required then you could break into the +ve line to the camera and use a PNP transistor to control power by switching it's base via one of the Pi's other GPIO pins.
If you can turn the camera power on and off via Pi commands directly then even better. Yoiu would just need to allow a small delay for the camera to initialise before asking for an image from it.
You can get dual mosfet powerswitches in an 8-pin dip for less than £1, with very low on-state resistance (RS, Farnell etc stock them). One of those would be handy to switch these two items on and off.
The battery pack looks reasonable, although I would be surprised to see it provide 15.6Ah useful capacity at 4.2 A after 50 cycles. Time will tell there