Swiss Half Fare Card

Jeannee, it works exactly as it says, you pay half fare (same as child's fare) for all rail, bus and boat tickets in Switzerland.
The tourist version, which is presumably what you would get, costs CHF 120 for one month. Details are here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-halffare-card.html

There is also a version for residents (which is what I have), which lasts a whole year and renews automatically. for that you need an address in Switzerland. This used to be available for 1, 2 or 3 years, but now renews automatically.

It doesn't matter which one you have, they both work the same. So just select "Half fare travelcard".

For trips within Switzerland, there is no point in buying in advance. Just buy on the day. If you use a ticket machine, press the the "Child/half far option", the ticket will be valid on any train that day. Your reservation would only apply to the train in Italy.

Yes, If you have a Half Fare Card, just indicate that when you buy the ticket. Don't worry about the "1/2/3" verbiage on the website. They don't actually collect your ticket, they just inspect them, and if it shows you paid half fare, you will show your Half Fare Card so the conductor can verify you paid the right fare. And since the Half Fare Card will have your name on it, you have to show your passport as well to make sure you didn't "borrow" the card from someone else.

You do this even if you buy tickets out of a vending machine. It will ask if you want the half fare price, and that is what you pay. Just have the card handy when the ticket inspector comes by. This includes any transport tickets, city trams and buses, mountain lifts, lake boats. These often operate on the honor system so you may never see a ticket inspector, but have your card and ID if you do.

Thanks to both of you!! It is what I thought but your validation makes me feel better about buying the ticket to Milan.