Administrative rights are only accessible to root, however if you want to delegate rights in that case you have to create something which is called roles and user need to be assigned to those roles. To find what kind of role is assign to individuals user you can try roles <username > to find the roles which are granted to the given user . roles which is given to user can be view into the file /etc/user_attr.
The contents of the following files coupled with a working understanding of Unix will provide the needed information.
/etc/passwd
/etc/group
/etc/sudoers (or /usr/local/etc/sudoers)
Database access depends on how the database is configured and your DBA can help you with that.