Hello Cata25
Well, unless you have family there, Zurich does not make a good base for your travel plans. You will spend time in trains which you could use to explore the country. Lucerne would have been better located.
The Half Fare Card is personal; each passenger who wants to benefit from discounts must have their own Swiss Half Fare Card. You would have to spend at least a total of CHF 240 for tickets per person to justify the purchase of the Swiss Half Fare Card. With your plans, it makes sense to purchase the Swiss Half Fare Card.
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/saver-day-pass.html
Titlis is not covered by the Saver Day Pass, you need a ticket for the cable car at either half or full fare from Engelberg to Titlis.
Saver Day Pass @ full fare: CHF 97 + CHF 97 + CHF 96 (Titlis ticket, full fare) = CHF 290
Saver Day Pass @ half fare: CHF 59 + CHF 59 + CHF 48 (Titlis ticket, half fare) + CHF 120 (Swiss Half Fare Card) = CHF 286.
There is currently the companion ticket special offer valid until 16 May. One out of three of you could travel with the companion ticket for CHF 39, provided someone else in your group has got the Saver Day Pass. The companion ticket has the same validity as the Saver Day Pass. The person using the companion ticket would additionally need a full fare ticket to Titlis from Engelberg at CHF 96. A Swiss Half Fare Card is not required for this person, though.
If you share all the costs, you will travel cheaper if one uses the companion ticket. Only one person can benefit from this offer as per Saver Day Pass, only 1 person can use the companion ticket. The companion ticket must bear the name of the person using it.
https://www.sbb.ch/en/campaign/companion-ticket.html
Kind regards,
Roland