Hi Stefanos,
For the password issue, you should be able to reset the admin password from the Portal as you are an Owner, see: https://learn.microsoft.com/en-us/azure/mysql/flexible-server/how-to-manage-server-portal#reset-admin-password
If you are using the MySQL 'Flexible server' you should have automated backups with a default 7 day retention period configured by default, more here: https://learn.microsoft.com/en-us/azure/mysql/flexible-server/concepts-backup-restore#backup-related-questions
However, once you have reset the password you should be able to do a manual backup also.
Hopefully this answers your question, if so please mark as accepted so others in the community can benefit.
Thanks