Hello Ciewhizoi14
You are already well informed and prepared. To use the SBB Mobile app with the settings made is a great idea, as by doing so, the app will suggest the best ticket options for your trip.
I gladly answer your remaining questions as follows:
Can I buy option 1 - Saver Day Pass CHF 49 with my tourist swiss half fare card?
YES
The price of CHF 49 is already a half price, correct?
YES
If I buy option 1, I can travel to zermatt from Basel at any time during the day and I can also travel to other destination within the day (or until 5 am the following day). Is my understanding correct?
YES
Option 2 - Day Pass for the Half Fare Travelcard at CHF 78. Is this price already a discounted price?
The Day Pass for the Half Fare Card is solely available for (Swiss) Half Fare Card holders. There isn’t a full fare day pass, besides the Saver Day Pass.
The only difference between a Saver Day Pass and a Day Pass for the Half Fare Card is price and the refund policy; the former is inexpensive yet cannot be refunded in case of personal circumstances that make a travel impossible.
Keep in mind, any use of electronic tronic tickets requires your physical passport or ID card, to be presented upon ticket check.
Kind regards,
Roland