Trains in Switzerland

"If I purchase a ticket departing Luzern at 0900 and thru the above towns, if we miss a connection, or just decide to stay in one town for a bit, can we take a later train without penalty?"

Affirmative

It is not quite so simple as that. There are different routes, and you may not get the scenery you want. If you go at 9:00 you will have the flatland train which misses the best views.

If your ticket is via the Brünig Pass - the scenic route, part of the Golden Pass - it won't be valid via Olten or Bern - not valid on that 9:00 departure.

If you want the tourist train the Golden Pass it only goes infrequently and if you get off you won't get another as the seats are reserved.

But if you get a ticket from A to B and take ordinary trains, as long as you remain on the route on the ticket, yes you can stop along the way.

Your card problems are likely because you have not set up 3-D security on your Visa card. The transaction will have been stopped by Visa, it won't have reached your bank. Call your bank and ask for it to be set up and then you will fly through. You did notify the bank before starting to buy the tickets that you would be making purchases in Switzerland?

Yes, its called "Verified by Visa" here in the States. You will have a PIN, and during the purchase process, you will be asked to enter the PIN. Ask your card issuer to set you up.
I have not tried it, but also downloading the SBB Mobil App on your smart phone seems to work as well. Need to have service on your phone in Switzerland when you are there, obviously.

I believe with a Saver Day Pass, you can take any trains in Switzerland in the GA area that do not require reservations (just the Glacier Express and Bernina Express trains AFAIK) for the day.

Kathleen, In Switzerland, you do not normally purchase a ticket for a specific time. You buy a ticket for a route, and the ticket is valid for any train on that route and that day. And you can get off the train anywhere and get on a later train, so long as you stay on route.
There is no discount for buying normal tickets in advance, you can buy them at the station on the day for the same price.

The route you have selected is not the quickest between Luzern and Geneva. If you just buy a ticket from Luzern to Geneva, it will be valid via the quickest route, which as Nigel says is through the flat (relatively) parts of Switzerland.
If you want to go the scenic route: Luzern - Brünig Pass - Interlaken - Zweisimmen - Montreux (spelling!) - Geneva, then you need to buy a ticket for that route.

If you buy a Saver Day Pass, that is different. That is cheaper if bought in advance on the internet. And it is valid anywhere in Switzerland, You can zig-zag across Switzerland wherever you want, and stop anywhere you want.
Info on Saver Day Pass: https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/1-day-travelpass/saver-day-pass.html

BTW - Montrose is in Scotland.

Thank you all so much. I have been trying to figure everything out for weeks--wish I had done this sooner!! I decided to opt for flexibility and get the Savers Day pass which I was able to get by downloading the app.
Again, I can't tell you how much I appreciate your time and input.