Databases outside of AlwaysOn availability group stuck in RESTORING status
How did you setup your Availability Group?  It sounds like what happened is you blanketed the backups and restores from the primary replica server to the secondary replica server.

In other words, you did a:

backup database &lt;DatabaseName&gt;
to disk .... &lt;so on and so forth&gt;


to all databases on the primary and a

restore database &lt;DatabaseName&gt;
from disk ....
with norecovery


to all the backups aimed at the secondary replica server (proper operations for future AG databases).  If you don't join one of those databases to the availability group then it'll stay in that restoring state.

The main question here is, if Database1 (for example) on your primary replica server as not meant to be in the availability group, then why would it be restored/existing on the secondary replica server to begin with?