Caravanistan

I don't know but it is true Asian travellers were targeted at Dushanbe Airport.

From your accomodation in Almaty, you can go for day trips by public transport and then hiking in the mountains. But November ??? In Kyrgyzstan, November is also late for the mountains. Southern Kyrgyzstan is somewhat warmer. So I think the best place would be Arslanbob, which has excellent homestay...

You can check out weather statistics on specialized sites, but not much difference
No, no snow on passes except high passes for hikers only

It is a dirt road but locals go there with ordinary (battered) cars. Certainly not worse than the Wakhan valley.

Peter Hopkirk The Great Game, well it is over Central Asia.

It is even possible to do it in one day by public transport till Pendjikent.
With a private transport, yes you can detour to Iskanderkul.

No, I think yurt camps will still be there.

Everyone generally arrives from Kochkor by the road from the East.
The main tourist yurt camps are located on the Northeastern shore. But it is possible to stay with some herders.

You can get most medecines over the counter in Kyrgyzstan and Tajikistan, except psychotics/narcotics and the like.

Between Dushanbe and Khujand, you have the Asia Express direct bus, or frequent shared taxis, leaving from the 'cement factory' North of town.