Best use of Swiss rail passes

I count 4 train trips (Zürich Flughafen (airport) - Luzern, Luzern - Mürren, Mürren - Zermatt and Zermatt - Zürich airport). You will also need mountain railways, but you can use your half fare card for that.
Note: Luzern is the German spelling, that is what the place is called when you get there. Lucerne is the French and English spelling.

No need to reserve for Luzern to Interlaken, or for any other train in Switzerland. There is a train every hour. Just look the times up on www.sbb.ch Enter Luzern to Mürren, enter date and time, and it will show you a train leaving at 05 minutes past each hour.
In fact, every rail line in Switzerland has at least one train per hour. Just look at the map you got ( http://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-netzkarte-schweiz.pdf ) and turn up at the station.

If you are hikers, 3 nights in Zermatt is not too much.

All these locations have dozens of marked hiking trails. You can buy good hiking maps at tourist offices, shops and possibly your hotel.

After using the pass for trains on those 4, full-coverage days, go ahead and use it for any other covered transport and attractions that fit into your day and evening (valid until midnight), including museums in the cities, lake boats, and any local bus or tram (all the solid lines on the Swiss map that comes with the pass). Yes, you do have to use day 1 of full coverage before you start using discounted days.

Thank you both so much! We will leave reservations as they are and hope for good weather in Zermatt!
One additional question: Not knowing what time we will end up getting into Luzern our first day I am wondering if we would be smarter to pay point to point from Zurich to Luzern on Day 1 and use our 1st day of our Swiss Pass on Day 2 taking advantage of the covered Mt Rigi trip? I am not sure if this is a possibility or whether we have to use rail travel to initiate our flex Swiss pass?

Mary, Yes, it is possible to do it that way, use day 2 (Rigi) as your first pass day.
But, as Laura says, the half-price doesn't start until your first pass day, so you would then have to pay full price from Zürich airport to Luzern (CHF 29, 2nd class) against CHF 46.80 (half price) Luzern to Rigi Kulm return. Looks like you save money with your plan.
You can look up prices on www.sbb.ch

Thank you. We will check weather report when we arrive, and depending on arrival time may opt tp do it that way. You have been most helpful!

I would look carefully at the prices for the Rigi Kulm trip. The price Chris F mentioned may be for the train via Arth-Goldau. If you want to do the boat--trail---cablecar--boat loop vis Vitznau and Weggis ( which is a wonderful trip) it costs considerably more---I am seeing full fare of 113 CHF for the loop.

http://www.rigi.ch/Travel-Information/Prices/Majestic-Round-Trip-Classic-Rigi-Round-Trip

So (since the Swiss Pass covers all legs of this loop) you would be better off using Day 1 of your pass for this---and paying the 29 CHF from Zurich airport to Luzern. You should be able to ride first class on the boats.

The Classic-Rigi trip sounds great. Do tickets for this trip sell out in advance or can we show up and go? Also since it will be the first day of using our pass, where do we go to activate the pass? Do we need to go to the train station?

Tickets do not sell out in advance as there are many departures and multiple legs to the journey. From Luzern your first step would be the boat to Vitznau. I honestly do not know where you activate your pass ; we have always done it at the Zurich Hauptbahnhof but I am sure you could do it at the Luzern train station. Since you have a first class pass you can ride on the first class deck on the boat to Vitznau.

At Vitznau, check the train schedule but you should have ample time to walk through town, or maybe skip one train and catch the next. The cogwheel train will take you to the top (Rigi Kulm) where there is a hotel restaurant if you are ready for lunch. Or walk around and enjoy the views over the lake.

Then you return by train as far as Rigi Kaltbad. There are nice level walks here if you want to spend some time at thus level before boarding the cablecar that takes you down to the lake at Weggis. There you catch a boat back to Luzern.

This loop trip is an excellent use of a covered day on a Flex Pass.