I've already removed the freeze when pausing for the same reason you mentioned. It's interesting how we had the exact same thought. Let me explain the timer:
In order to win a level and progress to the next one you have to:
1. Do all your tasks before the deadline.
2. And after finishing them, survive until the timer runs out.
I have decided not to show the state of power to the player. It is not usual for the power to run out. Turning on all lights or using the computer drains the power slowly. It is meant to catch the player off guard. After it runs out, the player will not be able to use any electrical device (including the computer)
I'm going to write the next devlog, soon. So wait for it if you want more details about these!