Day 15-16: Zurich. We will stop by Bern on the way from Grindelwald to Zurich. I believe there are lockers at Bern station for us to keep our luggages. Will be flying off on 16th morning">>
There are luggage lockers in Bern main station
raileurope.com/ europe-travel-guide/switzerland/ bern/train-station/bern-bahnhof-train-station.html
That looks like very nice itinerary. The forum moderators, Arno and Annika are able to comment better than I, but based on my experiences over the years, it should all work. Some of your days are quite full, (e.g., paragliding near Luzern)and I would spend time on the SBB web site to make sure that the transport is available to fit around your plans.
On days four and five, you probably should allow most of one day for the Bernina Express round trip. Keep your camera handy near Brusio. When we did it, some years ago, we had trouble finding a decent spot for lunch near the station in Tirano. There is enough demand that there are probably nice places, but we had trouble finding one just by walking around. Plan ahead? '-)
The whole trip is quite scenic, and the only "short cut" might be to start and finish at Pontresina. By the way, the scenic walk from Muottas Muragl to the lift station above Pontresina is justly famous.
I'm not sure, but , to me, "trekking " implies multiday hikes wit overnights along the trail. Is that what you mean?
If I were making that trip, I would add a bit of time in the Berner Oberland to do some more walking in that very spectacular region. Not sure what I would take out...isn't that always the problem? '-)
The next link to a very good post on this site describes a variety of trails and multi-day hikes.
This My Swiss Alps web site offers good information about hiking and various destinations/regions. I have not got the links memorized yet, but if you start on the home page, you can easily find that kind of information.
Two useful sources for hiking which this site will also lead you to, are the Switzerland Mobility site, with detailed route maps, places to stay, interesting features along the way, etc., and the SwissTopo site for good topos of all of Switzerland. On that site, click on the map at the right side of the home page. On the Switzerland Mobility site you may need to enter specific town names in the search box, although there is a regional selection menu.
swisstopo.admin.ch/ internet/swisstopo/ en/home.html
Tourist info in Luzern is by track #1 at the Hauptbahnhof. They can point you to a store with a good selection of maps, including hiking maps (Wanderkarte) with marked "Wanderwege" (Hiking trails.).
I like to use paper maps, but there area lot of on-line map services , also for smart phones.
I use Orell Füssli about 50-75 meters from that side of the station. Book stores have a hard time these days, so I'd double check at the Tourist Info.
In Zürich main station , Barth Bücherei is just down one short flight of stairs near tracks 1 and 2.
The Glacier Express requires reservations. On our trip a few years ago, the restaurant car also required a reservation. As you note, "regular" trains follow the same route, without the panoramic view cars.
I suspect that the Bernina Express might require reservations as well, but I am less certain about that.
You picked a good time of year, with the best chances for good weather. Early September is , perhaps, better in the Berner Oberland than late September, but usually the trails are good into October.