1)As long as u use dbconsole but not grid control, u should check not the agent but if the console is running
emctl status dbconsole
That will show if the console is running and the address where it listens
2)The backup is run not in the name of the user owning the Oracle software, but in the name of the user, specified as a preferred OS user credentials in the dbconsole of the database, so there is no reasons these users to be equal. Go to the upper right corner of the dbconsole home page and click preferences. Find the preffered credentials and change the preferred credentilal for the host OS user, then delete and resubmit the backup job

Regards