Lots of good questions, but I can only start to answer. More later, and others will likely comment.
By the way, welcome to My Swiss Alps. Nice to see that you have been reading.
Perhaps you know the English expression- "To make a silk purse out of a sows ear."
Traveling in Switzerland in November is more like making a good rucksack out of pieces of good fabric, but bringing your own boots. ;-) Silk purses require travel in ski season or hiking season. ;-) And, you start with better than a "sow's ear" at almost any part of the year
But,it is certainly not the best season for enjoying the higher alpine regions on foot.
The higher alpine regions are still open by some public transport, but many of the expected tourist attractions or travel facilities or are not running are not open. They tend to shut down in late October and open for ski season at around December 15th.
Using the timetable helps a lot to understand the options, as well as a map.
Read the intro page.
Play with the "points of interest."
<<"Lungern (which I heard is between Interlaken and Lucerne),">>
Nothing special in my opinion. What have you heard about it? Good friend lived there for many years....
Lower altitudes are completely passable. Above 2000 meters, maybe 1600 meters, better check, if you want to hike. That means that the Luzern area has promise.
For snow activities, Arno and Annika can help more than I.
Luzern has a great variety of attractions and options.
This link shows one hike (and discusses others) which are also surely available with no snow in November:
My own experience is that somewhere above 1600 or 2000 meters, I start panting on the uphills.
(By the way...the Swiss think a level trail is anything between uphill or downhill by about 30 degrees. Just joking, but "level" is uncommon.)
A couple of days above 1600 meters makes difference for me, but I don't "train" I just go there and work at walking or hiking.
You'll not likely be able to access trails above 2000 meters or so, but the moderators (Arno and Annika ) can refine that comment. Of course, you can always climb up to those places, but the hiking trails to get up there may not be open above, roughly , 2000 meters.
This map is the best detailed topo:
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&layers_visi bility=false,true&X=15 7160.00&Y=637800.00&zo om=6.
Others may comment on your diverse suggestions/questions.