Very Confused!

I would not trust anything you posted concerning Oh 'reallys.

Can you determine if it is charging, or not, and when? Can you rig, even temporarily, a voltmeter so you can monitor system running/ charging voltage?

First thing I would do is make sure the battery is charged, (on a charger if necessary) and take it somewhere to be load tested. You want a real carbon pile load tester, not some toy someone carries in their shirt pocket

Then if you can determine the battery is in good condition, you can move on the the charging system.

If you are unaware, the factory ammeter show show charge ( to the right) after starting engine, and should "taper back", generally to center and hover pretty much at center after getting the batt up to normal

A voltmeter, if you can rig one, should run about 14V when driving off idle.