Partial answers, I am not going to do the arithmetic for you.
You could get a Swiss Pass, or a Half Price Card (CHF 120), and pay half price for all your tickets. Probably a Swiss Pass, especially as it gives you discounts on mountain cable cars which you probably want to go on. But add it up yourself.
How exactly do the passes work if you are coming in from another country? Does the Swiss pass kick in once we cross the border and then we have to buy it then?
Yes, it starts at the border, as long as you already have the pass in your hands. You could get off the train at the border, buy your pass and get on a later train, but it is easier to buy it ahead of time, for example on the Swiss Railways website: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html
The map showing where the pass is valid is here: https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-sts-pass-gueltigkeit.pdf
"From Freiburg Germany to Lauterbrunnan (will be staying in Murren)" - You need to buy a ticket from Freiburg to Basel (border station, see map). Your pass is then valid from there to Mürren. It does not give up at the bottom of the valley in Lauterbrunnen.
Also covered or discounted are the railways and cable cars above Mürren and Wengen, see map.
"From Interlaken to Montreaux (on Golden Pass train to Montreaux) Alternatively we could just go from Interlaken to Chamonix and not take Golden Pass." - the Golden Pass is a route, which like all Swiss rail routes has one train per hour. From Interlaken to Chamonix the quickest route is via the Golden Pass route and Montreux, you can take any train on that line and see the same mountains.
"From Montreaux to Chamonix Mount Blanc" - You are covered up to Chamonix (see map).
"From Chamonix to Lausanne" and "From Lausanne to Luzern" - both covered. Also covered are lake boats.
"From Luzern to Munich" - The pass covers you to the last Swiss station (St. Margrethen), you need to buy a ticket from there to Munich. You do not need to get off the train.
