Find My first: This is a precaution against the repair requiring, for example, mainboard replacement. Also Find My's purpose is to enable tracking in the event of theft, so should not be needed whilst in the Apple Store. I would not have any qualms about that.
Password: This would be so that they could log in to the computer to run diagnostics. Removing (or giving them) the password involves a matter of trust. Do you trust the Apple Store to do the right thing? And what is the value or privacy status of what was on the Mac?
If it were me, I would have removed it from iCloud and Find Me, erased the disk and installed vanilla macOS before taking it to the Apple store. It is straight forward to recover from your backup afterwards.
Regarding backups, it is important to have a good backup before taking to the Apple Store as Apple may need to reformat the disk (depending on the fault) and Apple makes it clear that the data is your responsibility.