Hi Fenn1902 -
Welcome to the forum.
<<"This is the first time we will be in Swiss. We are so excited! ;) We need your help greatly because we have questions regarding the places. Our main focus is the alps/mountains/valley kind of sightseeing and not city sightseeing">>
I do not have any specific comments for you at this time. I do have one general one. It seems to me that you have included a fair amount of "city" in your itinerary. Bern is a really nice town, and I love to visit it. I go up to the Rose Garden almost every time I am in Switzerland if I am staying within easy travel distance of Bern. In early November, there will be some flowers still blooming, but nothing like there are in the warmer months. You will not be going for the flowers. Nonetheless, in my opinion, the view of the city from up there is worth the time, even later in the year in mid-Winter. But Bern does not really showcase mountains and valleys. Yet, you have a large fraction of your time there, and some in Luzern city.
Your time in Luzern and nearby could be longer, to appreciate the mountains, although you can certainly see them in the distance and closer by ( Bürgenstock, the Rigi, Pilatus). A walk along the waterfront to the Transport Museum gives you some views of them from various angles. Your plan to go up on the Rigi is a good match to your goals. For scenery, take the slower routes via Vitznau or possibly Weggis (connection from public transport requires a bit of an uphill walk to the lift station, but the ride up in the lift is really nice). I think the less scenic route from Luzern via Arth Goldau is faster, but I'd have to check the time table from Luzern to Rigi Kulm by all routes.
A map may be helpful:
However, if you were able to spend more time in Luzern, you might find time to visit Pilatus briefly ( don't need much time at the top unless you eat up there) as well as going up on the Rigi. That would give you a variety of views of mountains and valleys and a beautiful lake. Also, a lake boat ride, particularly at the southern end of the lake, would achieve your goals. You could include some of the northern part of the lake on a boat to Vitznau, for example, if you have enough time.
Bern is reasonably close to Interlaken and Luzern by train. It is easy to reach it from those cities.
Interlaken is a good base for the Lauterbrunnen valley and the other places you have listed. You would get a better feeling of the Alps if you were to stay further into the valley, at places such as Wengen, Grindelwald, Mürren and even Lauterbrunnen, but you are a half an hour or more from the "base" at Interlaken.
My feeling is that you would find it easier to meet your stated goals by staying in Luzern and Interlaken, and then visit Bern as a day trip.
Or, to meet your goals, you might wish to expand your time in Interlaken, spending more time visiting the mountains and valleys nearby. And, you might visit Bern from Interlaken or Luzern, since it is about one hour away by train from each one. Or, even skip it.
Your proposed itiinerary is quite nice, but is might not be the best possible match to your stated goals.