You could do the job with the circular saw, working with a straight-edge guide clamped relative to the board being cut.
But first make sure there are no hidden bits of nails/screws/tacks in the wood.
If you actually needed/wanted to tuck carpet edges under something you could just fix 1x1 battens at the edges of the area to be carpeted.
Unless the loft is frequently accessed, a carpet could be simply loose laid with no fixings.
Can you reconfigure the system to work without the glass-break sensor? If so, and the system then functions correctly, you would know the fault lies with the glass-break sensor.
That is a double socket. A plug is what fits into it. If the socket has no power then the circuit breaker at your consumer unit may have tripped (or fuse blown, if it's an ancient consumer unit).