Hello Judy
It is good to contact us as your research contains some confusions and wrong information.
There is no ticket named Super Saver Day Pass. There is the Saver Day Pass, which allows you to use any Swiss public transport system service at will on its day of validity.
And, there is the Super Saver ticket, which is a point-to-point ticket valid from station A to station B yet only on a specific connection; if you miss that connection due to a late arrival by air, the ticket is lost.
I guess you are intending to take the Saver Day Pass. Yes, with this ticket, as mentioned above, you can use any train, even an earlier one. Kindly note, for an ID-check upon ticket check, all e-tickets and passes need your physical passport, or state ID card, or driver licence.
The Swiss Half Fare Card for tourists is CHF 120, not CHF 190. The latter is for residents. The Swiss Half Fare Card is well worth if you will spend at least CHF 240 on public transport tickets per person. If your main purpose to visit our country is skiing, and all the trips you will do is Zurich Airport - Zermatt - Zurich Airport, no, the Swiss Half Fare Card is not worth to be purchased.
However, I suggest you to save the Saver Day Passes as soon as practical. The cost for it is raising the nearer the date, and the higher the demand for a particular day. Right now, the Saver Day Pass is at CHF 52 for 2nd March, which is the lowest possible fare for full fare Saver Day Passes - grab it now!
And, having worked at the airport for many years, I would say, you are fine to take the 11:45 a.m. connection from Zurich Airport to Zermatt, requiring one change at Visp.
For Saas Fee to Zermatt, simply purchase a full fare point-to-point ticket as a Saver Day Pass would mean an overkill. For this connection you could even purchase a Supersaver ticket as the timings are safe, as you say yourself. Right now, a Supersaver ticket is available for CHF 32 for an adult.
Does that make sense?
Let us know should you have got more inquiries.
Best wishes for 2024,
Roland