You don't have to sign the bill, otherwise you may be asked to write your own name. Those who cheat in the self-study exam will be disqualified. It's no use worrying now. If you don't get any grades, you will be considered cheating.

Don't worry if the teacher doesn't find out. Usually he doesn't check videos. The video is saved with the evidence. If he didn't find it on the spot, he wouldn't check the video afterwards.