The hotel lost its room card, and the hotel asked for a deposit of 100 yuan, saying that it was the manual fee for changing the lock and asked the hotel to pay it. ...

1\ is unreasonable. First, they didn't announce the price. Second, losing the card has nothing to do with changing the lock. Third, they don't write bills.

2\ You can pay the money, but you should explain the reason. I can't explain why you want them to write you a receipt. If you have time, go to their front desk for a chat and see the reaction of other guests. If there is no time, report it to 1 10. More importantly, you should call the local tourism bureau to complain.