Is it possibile to downgrade from 1.10 to 1.9.15 whitout any data loss?
There is no downgrade mechanism in osTicket. You would have to restore your database from your back up you took prior to upgrading.
So is not possibile to leave the actual 1.10 database with the old 1.9.15 files?
Anything is possible. But things would not work right in this case.