In family sharing, can my child have a different password for his apple id?

Yes.

Read about a child's ID and some special features: Create an Apple ID for your child - Apple Support

Click on this link to learn how to 'Change your Apple ID password' --> https://support.apple.com/HT201355

"After you change your Apple ID email address or password, you might need to update your sign-in information with any Apple services you're using" Click on this link to read "What to do after [or before] you change your Apple ID email address or password" --> https://support.apple.com/HT204071

- If you use the "Find My" feature disable Find My before changing your information, change the information, then reactivate it with the new information.