If i deactivate a user in production, will it still be possible to login to Sandboxes created by this user? Or does it make any automatic deletion of sandboxes?
Yes, you can definitely log in to the sandbox even you deactivated the user in production because both user instances are different. If you want to deactivate the same user as production, you need to freeze that user in the sandbox. After deactivating the user you are restricted from login into the sandbox.
Note: If you refresh a new sandbox after deactivating a user then the user is deactivated in the new sandbox instance.
Let me know if you have any doubt.