Where are you getting these errors and can you post the error itself?
I want to either expand the Db
The size of your database will be limited by your host, not EE.
or delete old events and registrations.
Whilst you can remove the old events and registrations, there’s currently no method to bulk delete those.
Events are gone, but transaction and registrations are staying.
Events are gone? EE wont allow you to remove the events if the event has registrations assigned to it (to prevent orphaned data). So are the events in Trash or have they been removed manually through the database as somepoint?