Thanks as always, @wanderweg.
I've updated my itinerary as below, with further considerations marked directly in the lines:
Day 1 - Arrive in Zurich at night (Sleep in Zurich)
Day 2 - Zurich (Lindt Chocolate Museum, Old Town walk, shopping for mountain area clothes) (Sleep in Zurich)
Day 3 - Depart from Zurich to Weggis: day trip to Mt. Rigi (Sleep in Weggis by the lakefront, or would Lucerne be better? -- Heard of a "Hotel Chateau Gutsch" located on a hill with view of the whole old town)
Day 4 - Take boat trip from Weggis to Lucerne, a quiet day walk in the Old Town (Sleep in same place as yesterday, whereever Weggis or Lucerne)
Day 5 - Depart from Weggis (or Lucerne) to Grindelwald, stopping by Lungern, Meiringen, Lake Brienz, etc. (Sleep in Grindelwald)
Day 6 - Take the train to Jungfrau, then back, passing by Wengen (Sleep in Grindelwald) [Note: If bad weather, swap this day with any arrangement from Day 7 or 8].
Day 7 - Go to Lauterbrunnen -> walk in Murren & Gimmelwald (Sleep back in Grindelwald)
Day 8 - Go to the lake area: Spiez/Oberhofen/Thun: Boat trip, castle + ice cream (Sleep back in Grindelwald)
Day 9 - Cable car to First and quick casual walk in the morning; depart Grindelwald for Zermatt in afternoon.(Sleep in Zermatt)
Day 10 - Day trip to Matterhorn, walk in Zermatt (Sleep in Zermatt)
Day 11 - Depart from Zermatt to Montreux, stopping by Sion, etc. (Sleep in Montreux)
Day 12 - Day trip to Geneva, stopping by Evian town in France (Sleep back in Montreux)
Day 13 - Day trip around Montreux, Vevey. The castle, boat trip, etc. (Sleep in Montreux)
Day 14 - Further day trip around Montreux [Note: any good suggestions for this day? Like Glacier 3000? Anything else?] (Sleep in Montreux)
Day 15 - Depart from Montreux to Basel, stopping by for a day trip in Bern (Old Town walk, museums, maybe some shopping) (Sleep in Basel)
Day 16 - Leisure day and rest in Basel, coffee time, visit some art museums. (Sleep in Basel)
Day 17 - Fly out from Basel (end)
Some specific questions:
(a) Is it worth staying in Montreux for the fourth night (Day 14)? Any better options if allocated to other areas? Or simply treat it as a rest day.
(b) Any better route suggestions for Day 6 to 8. Specifically, I want to cover Murren, Gimmelwald, Wengen and etc.
Thanks for any suggestions!