3 Swiss Pass Questions (reservations, when to purchase and what if going to another country)

If I have a pass, then does that mean I don't need any train reservations (except for special "Glacier Express" type scenic trains? ) I just show up, and there should be some non-assigned seating available?

Yes. exactly. But when you get on you will sometimes see where people have reserved seats.
Usually families or groups that want to sit together.

I'm still figuring things out. How long can I wait to purchase a pass (can I just get it in Switzerland once I land at the Geneva airport or arrive at a Swiss train station from somewhere else?

I bought mine right at Geneva Airport which has a train station. It is boarding pass size and comes in a plastic cover.
There is no need or benefit of buying the pass in advance. You can also make seat reservation online without it for say the Glacier Express. I made one for the Golden Pass Train like a week in advance. The earlier the first choice of seats.

If I dip into Annecy France (but start in Switzerland....how does that work? Can I still just show up w/o a reservation, show my pass and get some sort of discount based on the Swiss part being 'free', and the...say France part needing to pay?

Just take the bus from Geneva to Annency it is much quicker than any train

https://www.flixbus.com/
or
https://www.ouibus.com/?utm_campaign=FR_17_acquisition_generique&utm_medium=1_comparateur&utm_source=rome2rio_flux

Before you finally decide on the Swiss Travel pass you need to cost all your Swiss travel using the Swiss Rail website, this has a default of half fare, so you may well find that your best bet is the Half Fare Pass valid for one month and costing 120CHF. Having said that answering your questions:
1. You are correct, you will find that most seating, if not all is non-assigned as you call it. Swiss transport is mass transit.
2. You can certainly buy the pass at Geneva airport or any other Swiss station with manned booking office.
3. Your pass will be valid to the border station, so you would need to buy a ticket at the start of your journey just ahow the pass at the ticket office and the clerk will do the rest.

Thank you. That helps a lot!

If I have a pass, then does that mean I don't need any train reservations (except for special "Glacier Express" type scenic trains? ) I just show up, and there should be some non-assigned seating available?

You never need reservations for Swiss trains, whether you have a pass or normal tickets. All seating is what you call "non-assigned" (except for those three extra tourist trains, and in those cases you can always use the normal trains on that route).

I'm still figuring things out. How long can I wait to purchase a pass (can I just get it in Switzerland once I land at the Geneva airport or arrive at a Swiss train station from somewhere else?

Buy at any Swiss airport or border station (including "Genève-Aéroport"), or online at the SBB website. Same price both ways.

If I dip into Annecy France (but start in Switzerland....how does that work? Can I still just show up w/o a reservation, show my pass and get some sort of discount based on the Swiss part being 'free', and the...say France part needing to pay?

A Swiss Pass is valid on Swiss lines only. So you need to buy a separate ticket from the last Swiss station to Annecy (and back again).
You can see what lines the pass covers on the Swiss Pass Validity map: https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf

And if you look at the map of validity, you will see that a Swiss Pass extends as far as Chamonix-Mont Blanc, should you wish to take that route to Annency.

Also, to adjust the information on reservations on Swiss trains: while they are not necessary, you can make reservations for IC trains. So when you board one of these without reservations, check for a reservation card above before occupying a seat.

What a great map and info. Thanks! This helps a lot!

You get a paper copy of that same map when you buy the Swiss Travel Pass in person.