I have more than 1 DBs in Exchange Server 2010. How to know which 1 to keep as it is creating problems when I create, delete or modify anything?

Check the health, check indexes, rebuild the indexes in case they are not healthy

Perform a fail over of DB's (if you can afford a little disconnection)

The Exchange store is a storage platform that provides a single repository for managing multiple types of information in one infrastructure. The Exchange store (store.exe) is the core data storage repository for Microsoft Exchange Server 2010