How Far In Advance To Purchase Swiss Rail Pass

There is really no advantage and possible disadvantages to buying a Swiss Rail Pass in advance. You should buy it if and when you arrive in Switzerland at the time you planned.

You can buy it at the Zurich Airport.

I would just buy passes at the airport. Its easy - the counter is just opposite Starbucks at Zurich airport. There was no line when I was there last summer. Just present your passport, Credit Card and you get the pass in a nice clear plastic wallet.

Margaret

There is no price difference for buying in advance. You can buy it at any airport or border rail station.

The only reason to buy in advance is if you are entering Switzerland by train and do not want to get off the train or waste time at the border station. In that case you buy in advance, for the same price, from the SBB website and you get a print-at-home version. You then buy a ticket for the "foreign" section up to the border station.
Website and prices here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html

Does this advice go for the Half Fare Card also?

The only advantage I see to buying a Swiss Half Fare Card in advance is that you can apply it to Super Saver Fares

Even with Super Saver fares it is not necessary to have it in advance. You do not need the Half Fare Card in your possession when you purchase the ticket, you just need to have it when you board the train.

Often there is a difference between the dollar price versus the Swiss franc price, due to fluctuations in the exchange rate. Usually (but not always) the price in Swiss francs is lower. But if your credit card has foreign transaction fees, you have to add that amount to the cost in francs.

Does this advice go for the Half Fare Card also?

You can buy it at a border or airport rail station, or online in advance on the SBB website, all at the same price (CHF 120 for the one month tourist version, see here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-halffare-card.html ). You do not need a ½ price card at the time you buy a ½ price ticket. You do need a valid ½ price card on the day you use the ticket, and must show both the ticket and card to the ticket inspector on the train.

"The" price for all passes and tickets is defined in Swiss Franks, and is fixed for the whole year. Resellers in other countries charge prices in foreign currencies and may well charge more.