Hi, and welcome to MySwissAlps!
>> 1. Should we make Bern or Lucerne our base and book a hotel near the train station there for the 3 nights, or possibly Interlaken?
I would prefer Luzern or the Jungfrau Region (Grindelwald, Wengen, Mürren or Lauterbrunnen). Interlaken is a good transport hub, and has a lot of shops and hotels, but cannot compete with the scenic beauty of the mountain villages in the Jungfrau Region. I like visiting Bern, but personally I prefer to stay in smaller towns and villages.
>> It appears that most hotels have very limited, if any, flexibility for cancelling so I hesitate to commit too early but also don't want to find ourselves without a room.
That hasn't been my experience. Cancellations can usually be made up until a week or so beforehand, or even up until the day before in many cases. The exception is usually when you book in advance at a discounted price, which is not refundable if you change your mind.
There will always be rooms available, but if you want the best choice of location and price, I would not leave it till the last minute to book a hotel, even in low season. The crowds will have gone, but many hotels will also close for a break, reducing the number of rooms on offer.
>> 2. Previous posts all seem to be against booking any tours or scenic rail tickets ahead of time in November due to the weather
That's true in relation to mountain transport for the whole year, not only November.
Scenic trains such as the Glacier Express have compulsory reservations that do sell out, so if you want to be certain of travelling on a particular date, you do have to reserve in advance. However, the Glacier Express will not be running when you are there. If you decide to travel on the Bernina Express, there is one departure per day from Chur, and reservations are compulsory, but could probably be made a day or two beforehand at that time of the year. You can also travel the same route on regional trains without a reservation. It is really too far out of the way for you though, given your limited time and other plans.
>> Is it realistic to check the weather first thing in the morning and still be able to book a tour or Jungfrau railway ticket for that day?
Yes, that is the recommended way of doing it - either the day before, or the morning of the day you want to travel to a mountain top.
>> Older posts suggested that a half-fare travel card may sometimes be needed with the Tageskarten day pass, is that your experience too?
That depends on whether you have bought the 1-day travelpass (Tageskarte) or Saver Day Pass (Spartageskarte). The Tageskarte is only valid if you also have a Half-fare card, but the Saver Day Pass can be used on its own. The Saver Day Pass is quite a new product, having been introduced only a few months ago.
There is more information on both cards, and a map to show where each is valid, on the following pages:
1-day travelpass (Tageskarte)
Saver Day Pass (Spartageskarte)
If it's the new "Saver Day Pass" you have bought, this discussion about its validity on mountain transport might interest you: