Help with Switzerland itinerary and Swiss Train Pass

Jules, that is a lot of questions. I will try and answer as much as I can. Feel free to come back with more questions to fill in the details.
I always think a good map is a place to start planning. This is the official rail map of Switzerland, showing all the rail lines (except for a bit of detail missing around the cities: https://www.swisspasses.com/railpass/overviewmap_en.pdf
It will show you what is and isn't possible. All Swiss rail routes have at least one train per hour. You can then get detailed times (and prices) from the Swiss Railways site: http://www.sbb.ch/en/home.html

Trains from Switzerland to Paris are easy. You can either exit Switzerland via Geneva or Basel, both 3 hours to Paris.
Is you visit to Geneva/CERN at the beginning or end of your circuit of Switzerland? If it is at the beginning, you could fly on a cheap airline to Geneva, circuit Switzerland, and then exit via Basel. Or, Train to Appenzell, circuit Switzerland, do Geneva last and get a train from there to Paris.
Current train times from Switzerland to Paris for both routes are here: http://www.tgv-lyria.com/sites/default/files/pdf/BROCHURES_CO/TIMETABLE-2016S2-fr_ch-TGV-LYRIA-EN_0.pdf

You will have to calculate what pass to get yourself. Eurail passes are restrictive on what they cover in Switzerland, but, Swiss passes do cover all lines except mountain cable cars. The map I posted above shows exactly what is covered.
The Golden pass train, like the other special trains, is an extra tourist train on a route that has regular trains. You see the same mountains whichever train you chose, and you are covered by Swiss passes.

That is enough for one post, please come back if you have more questions.

I am ending our Switzerland travel in Geneva.

I will probably start in Appenzell as I will be coming from either Munich or Salzburg.
I am not sure I am not sure if I should go Appenzell to Luzern to Bern to Interlaken area or go to Interlaken before Bern.
There are specifics of the train that I probably need to talk to the train people but cannot find any kind of phone number. I would wait until I arrive to purchase a ticket except that I am arranging lodging so I could end up booking a route that doesn't make sense in terms of purchasing train tickets. In France, I save a lot of money by prepurchasing tickets. I am told this is not the case in Switzerland. And part of the appeal of the Swiss train pass is the museum, tram, gondola freebies and discounts but it is not clear if I can use them on just the days I travel on the train (if I purchase the flex pass)

I am not sure I am not sure if I should go Appenzell to Luzern to Bern to Interlaken area or go to Interlaken before Bern.

If you look at the rail map I posted last time (or look up on the SBB website), you can see that in order to get to Interlaken you need to go via Bern, except if coming from Luzern. How long do you want to spend in Bern? Most of Bern can be seen in one day, and you can do it as a day trip from Interlaken/Berner Oberland; or stop off en route and leave your luggage at Bern station.
And, most people (including me) recommend not to stay in Interlaken, but one of the places further up the side valleys (Lauterbrunnen, Mürren, Wengen, Grindelwald, ...).

There are specifics of the train that I probably need to talk to the train people but cannot find any kind of phone number.

What specifics, what train people? The main railway company in Switzerland is the SBB (=Swiss Federal Railways). They have a website ( http://www.sbb.ch/en/home.html ) and they do have premium rate phone numbers you can call (on the website), but that will cost. You best bet is to research times and prices yourself on the SBB website, or ask here or on other forums.

I would wait until I arrive to purchase a ticket except that I am arranging lodging so I could end up booking a route that doesn't make sense in terms of purchasing train tickets. In France, I save a lot of money by prepurchasing tickets. I am told this is not the case in Switzerland.

Correct, SBB (and the other Swiss Railway companies) have a different pricing policy to SNCF (French Railways). There are some advance purchase "Sparpreis" tickets available in Switzerland for lightly loaded trains, but in general there is no discount for advance purchase. Same price for all trains, no advance reservation, no "booking", tickets are valid on any train, just buy tickets on the day and get on the train. You have 3 choices:
1) Pay full price, as shown on the SBB website.
2) Buy a half price card (Halbtax Abo) and buy half price tickets, prices on SBB website.
3) Buy a Swiss pass, then just get on the train, nothing more to pay.

The SBB website (and other railway company sites) always show the fastest route, and the price for that route. If you want a different slower route, you need to add "via" locations to your query.

Awesome, thanks! If you have other insights into the cities I'm thinking of this info is so helpful. I will plan on one day for Bern and I will go there from Luzern. I was thinking of staying in Grindewald and perhaps one other city in that Interlaken area. Perhaps Murren or Grimmelwald? I'm not going to be there for skiing and I don't necessarily need to be where the "fancy" people are. I like smaller and charming. I was thinking of doing some sledding and perhaps trips up to the top of mountains for views and/or a meal.

In regards to the Swiss pass, it apparently includes a lot of local transportation like trams, postal buses as well as museum admission. So if I buy a regular Swiss pass for 8 or so days, I will have pretty much all transportation covered for that time period. However, I will probably only need trains for half of those days, if that. However, if I buy the "flex" pass, so 4 days, but stay in Switzerland 8 days, I'm guessing I don't get the "extras" on the days that I'm not traveling by day. But that is just a guess. In any case, it is so helpful to know that the prices I'm seeing for train rides are the actual prices I will see in January. That makes it easier and I will just add up all those segments to see if it makes sense to do a pass. Thanks

Do you know if I can just buy a Geneva-Paris train ticket thru SNCF even though I'm starting in Switzerland? I'm also wondering the same about Salzburg to Munich. The Bayern tickets are a huge deal for groups.

I really appreciate your help. I do like to do a lot of planning so I can make the most out of trips.

Do you know if I can just buy a Geneva-Paris train ticket thru SNCF even though I'm starting in Switzerland? I'm also wondering the same about Salzburg to Munich. The Bayern tickets are a huge deal for groups.

Yes, you can buy Geneva-Paris through the SNCF site. There are 29 EUR tickets available now.
If you plan on using a Bayern Ticket, just buy it from a DB vending machine in Salzburg Hbf before you travel.

I'm not going to be there for skiing and I don't necessarily need to be where the "fancy" people are.

I don't know what to think of that statement, since I've been to Wengen in January for skiing and definitely do not consider myself "fancy". But if you do want to go for sledding, or just sight seeing on the train, it works, as does Muerren. Gimmelwald will be D-E-A-D.

I was thinking of staying in Grindewald and perhaps one other city in that Interlaken area. Perhaps Murren or Grimmelwald?

These are not cities. Grindelwald is a tourist orientated town, as is Interlaken. Mürren (spelling) is a village of a few hundred people. Gimmelwald (spelling) is even smaller. Do not expect city level facilities.
In January, these places are all orientated towards skiers, but in Switzerland, these are not "fancy people", everybody goes skiing, but they pay Swiss prices.

Do you know if I can just buy a Geneva-Paris train ticket thru SNCF even though I'm starting in Switzerland? I'm also wondering the same about Salzburg to Munich.

For Geneva-Paris, you are not starting in Switzerland. SNCF starts at Geneva station, it is a French railways route, and French fares apply (discounts for advance purchase, all tickets must be purchased in advance and are only valid on the train for which they were purchased).
Salzburg is the border station between ÖBB and DB (Austrian and German Railways). DB fares and rules apply between Salzburg and Munich.

No need to guess - it is correct that the Swiss Travel Pass Flexi version does not give you any extras outside of the 4 counted travel days; see https://www.ricksteves.com/travel-tips/transportation/trains/switzerland-rail-passes. If you buy the version with added Half-Fare Travel Card for $63 more, then you'll get the lift discounts or half off other transport on your in-between days, but no museum coverage. If using a Eurail pass for Austria and Switzerland, then the lift discounts provided by that pass do apply on in-between days. Both passes fully cover the Golden Pass trains; a seat reservation is optional on the Zweisimmen-Montreux portion. As I mentioned on your other thread, if your time in Switzerland fits into 8 consecutive days, then that's the most convenient and complete coverage version of the pass. Count those days through your arrival in Geneva, but not the train departing toward Paris.

P.S. For transport costs around the Lauterbrunnen Valley in chart format, see www.jungfrau.ch. For instance, Muerren to the top of Schilthorn is 80 CHF roundtrip in winter, or half-price on a Swiss Travel Pass travel day (or 25% off with a Eurail 2-country pass).