Welcome to Switzerland.
Yes, you can.
Kindly note, in order to buy tickets using the app, in a first step, you have to add the second person (or further persons) as co-traveler(s). See the option on Profile tab.
It is important that you buy tickets for each person individually. Each ticket must bear the name of the traveler who is using it. Each person must show an ID or passport during ticket check.
What concerns the Swiss Half Fare card, you can either print it or display it as PDF document on your phone. Provided you bought the Swiss Half Fare Card with your account, it is even displayed in your SBB Mobile app.
Let us know if you have further querries.