I’ve done it in the past, once or twice. I suppose it helps but it sure makes a helluva mess, especially Arctic Silver. It might be alright if I absolutely knew I wasn’t going to be taking it apart ever again, but we both know that’s not going to be the case.
I’ve stopped doing it - the mess just isn’t worth it. That stuff gets on everything.
You need electrical conduction at those threads, not just heat conduction. So, maybe thermal grease will work, maybe it will not, not sure. I've used it occasionally on those threads, but sparingly, sometimes in addition to an electrically conductive agent like DeoxIT, CRC 2-86, etc. Also I got some pricey thermal and electrical conductive (supposedly) grease I've used on those threads.
I use Nyogel as well, but not on the pill threads, but the tailcap and body threads and it doesn't seem to interfere with electrical conduction, even though it's not electrically conductive.
Depends on the host and what the output will be. Always with those emitter shelf, disc types. But use non setting compound, on a couple of occasions even tried to add silver powder to the compound to try to make it better. Not sure if that made any difference.
On the threads, no, it will not help. The contact area is too small/too localized, and paste thermal compounds don't work unless the layer is very very thin. Using it to fill gaps will do nothing but make a huge mess.
Where you have a flange on the pill that seats against a flat area in the head, sure, use it there. But not on the threads.