Does the Swiss Travel Pass work if based in Chamonix and going to various places in Switzerland

A Swiss travel Pass can be used in either direction on the rail line between Chamonix and Martigny.

See the official validity map here: https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf.sbbdownload.pdf
It says: "The Swiss Travel Pass and the Swiss Travel Pass Youth entitle you to: –– unlimited travel on all train, bus and boat routes marked on this map with a continuous line"

It cannot be used on any other transport out of Chamonix, neither by rail in the other direction, nor by bus to Geneva.

I don't know whether you can buy a Swiss Pass at Chamonix station, it not being run by a Swiss company. You may have to buy your passes online in advance at the SBB website here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html
The price is the same online or at a station.

Yes, you'd have to buy the pass before arriving to Chamonix - and within 6 months of the pre-validated start date.

Thank you for the information. I have two more questions: 1) what do the dotted lines on the Travel Pass map mean and 2) how do you get the Family Pass? We will be traveling with two children age 12.

There are dotted lines and dashed lines. The dotted lines indicate mountain transport ( lifts or trains) that are not fully covered by the Pass, but you get a discount of 50% or 25% ( there is a keynto which).

The dashed lines are where the train goes through a tunnel.

You get the Family Card by requesting it when you buy the Swiss Passes for the adults.

Yes Swiss Travel Pass can be used in Chamonix

One of the many bonuses of the Swiss Travel Pass is that it does cover travel to Chamonix via the 'Mont Blanc Express' (even though Chamonix is in France).

A connection from Geneva to Chamonix would take about 2 to 3 hours in duration and involves 2 train changes along the way; once in Martigny and then once in Vallorcine. The portion of this route between Martigny and Chamonix is known as the Mont Blanc Express.

The trains comprising of this connection don't accept reservations, so the Swiss Travel Pass is all you would need to board.

https://www.myswitzerland.com/en-us/tickets/swiss-travel-pass.html

Are you sure you want to do those as daytrips from Chamonix? Chamonix to Zermatt is 4 hours each way. Chamonix to Montreux is not as bad, but still 2.5 hours.