Can a child of two and a half weeks stay in a hotel without an account?

yes. As long as everyone accompanying you has registration information.

hotel check-in requires a certificate for each person, that is, as long as there is a photo of me, valid and legal personal identification, such as ID card, passport, visa, military officer's card, police card, zero-hour ID card, etc.

if you don't have relevant certificates, you can have relevant identification certificates issued by the police station.

babies who are not registered do not need documents.