Will you lose your balance if you turn off or update NiceHash Miner or if you shut down or restart your PC?

The short answer is no.

Your balance is linked to your Mining Address at NiceHash. You can turn off NiceHash Miner at any time, update it, turn off your PC and later come back to mining. Do note, however, that your balance will not increase when you are not mining (when your PC is turned off or when your NiceHash Miner is not running or is not active).