Do these have a solid ON/OFF switch? meaning, if I turn them on, and then unplug them, will they still be on when you plug them back in. If you hook them up to an outside switch, will it still be on when you toggle the power?
Yes, there’s a mechanical switch on each light. See below. 
I plug these in when I have a zoom mtg. Family barges in and then quietly backs out…
The pleasant grinding noise of the motors doesn’t bother you?
Nobody hears it on their end. Actually only one of the lights makes a decently loud grounding noise so I sometimes leave it off. The other is surprisingly quite. And i can ignore it.
I mean if these automatically went off when there was a woot off I’d buy one for every room 
As soon as they make an API, I’ll make an app for that
Since these have been around for a long time, I have to ask, what’s inside -
LEDs or incandescents?
Do they get warm?
I think they’re little LEDs. They don’t get warm any that I recall.
I need another set. I used these to mark the edges of the table when I DJ parties. No more people knocking my gear around! Yay!