Hello Thubeefai94
The Swiss Half Fare Card offers the same validity and amenities as the Half Fare Card. The only difference is, the former is for tourists, the latter for residents.
Consequently, yes, you can purchase the Day Pass for the Half Fare Card (and Saver Day Passes), too.
You do not need to validate the ticket as it is valid for the day which you had chosen during purchase.
Enjoy your time & best wishes,
Roland