From Murren to Zermatt and Lausanne/Montreux

Regional train has nothing to do with it in Switzerland. No trains need reservations except special named sightseeing trains like the Glacier Express or Bernina Express, which should not factor in your route. Just be sure not to board the Glacier Express in Zermatt when you are leaving. It will look very different from the regular trains and I'm sure the conductors standing on the platform will warn you off anyway.

If you are in Switzerland for 10 nights, then you will be there 11 days total. That would indicate a 15 day Swiss Travel Pass. If you add up the cost for these trips, you will probably find that a 30-day Half Fare Card will save you the most money, but you will have to buy a ticket for each journey. You get 50% discount for everything, trains, buses, cable cars, urban transport like in Lausanne. You don't say how you are getting to Switzerland and how you are leaving.

Thank you so much for your prompt response, Sam. As you pointed out, Half fare card seems the better choice. We will fly in and out from Paris. We will arrive in Sils Maria, near St Moritz from Insbruck, Austria. On the way back, we plan to stay in Lausanne for two nights before returning to Paris to fly back to the US.

If you are going from Paris to Switzerland, I assume you will be taking a fast train from Paris to Geneva (or Zurich) and back?
Those trains you DO need a reservation for, and the sooner you buy the tix, the cheaper the price.
Lots of info on this at www.seat61.com

Going from Lausanne to Paris, you can get advance purchase nonrefundable, non-changeable tickets for the direct TGV for as low as 34 CHF per person. Buy these as far ahead as you can to get that price. It will be a better deal than anything using the Half Fare Card.

From Innsbruck to Sils Maria, you can take a train route via Sargans and Chur. Again there advance purchase options as low as 56 CHF, or 69 CHF using Half Fare Card and buy anytime. There is also a more direct route with a train to Landeck-Zams, then bus to Martina, then bus to Scuol-Tarasp, then train to Zernez, then train to St Moritz, finally bus to Sils Maria. Can't get a cost for that one now, probably not too much with a Half Fare Card.

Thank you so much for your help,Shoe and Sam. I have just bought two tickets from Lausanne to Paris for 58 Euros for two. It is a very good deal,indeed. Actually, I got these tickects from the French website en.oui.sncf/en. I had checked the Swiss website, but it was mote than double the cost of the French deal. For the trip from Innsbruck to Sils Maria, the cheaper tickets may have gone.
I am still trying to determine whether I would buy the Half Fare Card or the Flex Card or the Swiss Card. This is so complicated for first time tourists to travel in Switzerland!. I went to the SBB.CH website to try to calculate the travel expenses, but I could not find the prices and when I checked May 26 from Lauterbrunnen to Zermatt, it kept changing to May 25. Was it me or the website? It is so time consuming without receiving good results!. Is it correct that the Swiss card has to be used on consecutive days and if one only uses once a day, it may not benefit much? and the Half Fare card can be used within a month and does not have to be on consecutive days, right?

Generally, Swiss don't sell advance tickets beyond 30 days. But prices will not change, so to check a price, just use a week from today. When you click on the red ticket icon, you'll see something like "price for 1 person plus Half Fare Card is XX.XX CHF". That means the price assumes you have a Half Fare Card, so you have to double that price to see it it will be without a Half Fare Card.

Edit, Yes the Half Fare Card is valid from the date of validity for 30 consecutive days.

I went to the SBB.CH website . . . . when I checked May 26 from Lauterbrunnen to Zermatt, it kept changing to May 25.

Did you enter a date AND a time? When you start the webpage, it defaults to the current time and date. If you change the date only, and you are in another continent so the current time is in the middle of the night in Europe, there will be no trains at that time, and it will find the nearest train, which may be the day before.
You can always click "Earlier trains" or "Later trains".

The price is fixed, all trains are the same price for the whole year, so it doesn't matter which date or train you check.

Is it correct that the Swiss card has to be used on consecutive days ...?

The Swiss Travel Pass is for consecutive days.
The Swiss Travel Pass Flex does not have to be consecutive days. Use it for the amount of days in the pass, as long as it's within the validity period of one month.

https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests.html

Thank you for all your responses. I am having a hard time with what pass I will need to buy. A Swiss pass would not work ,I know for sure because we would not on the train every consecutive day. Therefore, it will come down to a Half Care card and a Swiss Flex Pass. I understand a Half Care card can be used for a month. However, I read somewhere that it has to be used on consecutive days. Is it correct? When I added all the main train journeys that we will take from St Moritz to Lausanne with stops at Luzen, Murren,Zermatt , the total amount will be CHF 160.05 for each person. The Half Fare card costs CHF 120 and the Swiss Travel Pass Flex ,CHF 445 for 8 days. Of course, I do not know how much, the cost will be for cable cars,cog wheel trains ,trams and buses when we explore Luzern , Murren, Zermatt and Lauzanne. The Swiss travel website My Swiss travel or something similar indicates that the Swiss Travel Pass Flex may not include some cable cars and mountain excursions.
Thank you again for your help.

The Half Fare Card lasts from the first date of validity for the next 30 days. Consecutive has nothing to do with it. If it starts June 1, the last day of use is June 29. Pretty simple.

Now you have made a serious error in your price calculations. It is a rookie mistake, because the prices on the SBB can be a bit misleading. For instance, St Moritz to Luzern says "1 x individual tickets, Half Fare Card, Total price 42.50 CHF" That means 42.50 is the price if you have a Half Fare Card. So without it, the cost is 85 CHF. So your estimate of 160.50 CHF is off by exactly half. The real price without the Half Fare card is 321 CHF. So if you got a Half Fare Card, your cost is 120 + 160.50 = 280.50 CHF. A 4-day flex pas would be 310 CHF, so you can see the Half Fare Card results in less cost.

Now you made this statement:

Most of the time, we will be in a village or city for two or three nights and we will use buses, cable car or trains,especially in Murren.

The Half Fare card will give you the 50% discount on these as well. If you get a Flex Pass, it can not be used on these days that are not travel days. Now the Schilthornbahn has been included this year with the Swiss Travel Pass, but only if you use it on the day you arrive or the day you leave (with a Flex Pass).

You mentioned getting an 8-day flex for 445 CHF to cover these extra days, but other than the Schilthornbahn, the other lifts are still only a 50% discount with the Flex pass, and the lifts above Wengen are only a 25% discount.

Hi Sam,

Thank you so much for your detailed explanation. I think I am leaning towards Half Fare Care,since it seems to make sense and especially it does not require consecutive days of travel. I appreciate your help and others'.