HELP with Storyline trigger controls

1. Trying to temporarily make tabs unavailable to trigger layers.
I've covered them with a no-fill rectangle, to be hidden when audio
ends. Doesn't seem to be working.

You're on the right track - covering them, then setting the state of the cover to hidden when audio ends.  The problem is that if you have an unfilled shape, there are no pixels inside it to intercept the click, which falls through to the tab. What you need to do is fill the shape, then make that fill transparent. Right click, choose Format shape, and set the transparency to 96 -97%. I've heard reports of it not working if set to 100%.

Another option is to set the tab with an initial state of Disabled, then change it to Normal when the audio ends.

When does the visited state of a layer get activated? Immediately upon
it's timeline beginning?

Any object with a visited state goes to Visited when it is clicked. It can be trusted to stay in that state until the slide is left. On return it is not always reliable.