RE: Stabillizer came loose, base stripped out???
If the insert itself is not stripped andit just came out of the bow then yes go ahead and epoxy it back in. It was probably pressed and glued in somehow from the factory so re-gluing it shouldn't be a problem. As far as a new stabilizer goes you can't go wrong with a doinker. I like the 4-6in versions for hunting.
Welcome aboard!