After looking at the links, I think my itinerary should be as below........
Day 4: Day trip to Bern from Interlaken
I like Bern a lot, but you may not wish to spend a full day there. Generally Luzern is worth more time than Bern. I know the forum moderators Arno and Annika usually make that recommendation. ( By the way, out of habit, I use the German spelling for Luzern, since it is in the German-speaking part of Switzerland.) There is lots to do in Luzern itself that is indoors. On the other hand, many of the attractions around Luzern are outdoors and you might not want to be walking or out in the countryside in Mid-December. Maybe a lake boat......Mid December is a time when it is difficult to predict the weather. I have had beautiful, not too cold days then, great for walking and sightseeing on the Rigi, for example. Or I have had awful and bitter cold days.
One of the attractions of Bern is a walk through the arcaded Old Town ( good in any weather) and up to the Rose Garden. Very few to zero roses there in mid December, although the view over the city is nice.
Bern is easily accessible from Interlaken, as you have noted, or, also , from Luzern.
I think if i were planning the trip, I'd tend to keep Luzern and Bern on adjacent days , so i could adjust my time between them. But, i would not be trying to sky dive at Lauterbrunnen. Interlaken, in itself, is not as interesting as either of those two cities. But, if skydiving is happening at that time of year ( and the moderators would know better than I ) then you might want flexibility to accommodate changing weather, and thus be near Lauterbrunnen.
<<"1. How long does it take to travel from Interlaken to Chur via the Glacier Express?">>
About six hours. Use the timetable, and put Andermatt in the "via" box.
That link to the Swiss Rail timetable gets you to a page where you can put in a "via" intermediate stop.
<<"2. Is 1 full day sufficient for Lucerne?">>
The precise answer is - "That depends" ;-)
In warmer weather, I can spend a week based in Luzern, visiting all of the attractions , going up on the Rigi and Pilatus, riding the lake boats, visiting some of the smaller villages around the lake, take half a day to ride the lake boat, funicular and walk to Hammetschwand, have lunch, and return......In cold weather, you can get a sample of the city itself in one day or even 4 hours, but you are only scratching the surface.
Walk through the Old Town on both sides of the river at least to step inside the Jesuit Church on the side nearest the station but mostly the main part on the opposite bank, crossing the river back and forth on different bridges. Walk to the Lion of Luzern, and visit the Bourbaki Panorama. Walk through the very small Picasso museum in the old town.. Get a bite to eat. Four hours.