You seem to be well prepared and well informed, congratulations on that.
No, the e-ticket together with your physical passport is fine for travel. Linking the Swiss Half Fare Card (SHFC) with the SBB Mobile app is only possible if the SHFC was bought from SBB, not from Klook. Show it as PDF saved on your phone instead.
My general advice is to buy tickets from SBB, there is no advantage when done so from Klook - in the contrary, SBB cannot help with tickets issued by Klook.
Furthermore, be careful when seeing cheap tickets on Klook, they are often so called Supersaver tickets and come with strings attached, meaning they are limited to a certain connection only. You will have to pay a new ticket if you use these tickets on other trains than indicated on the ticket.
For children below 6 yrs of age, a passport proving their age is sufficient in case of doubts. No other ticket is required.
Yes, you simply buy a half fare ticket for the respective class in which you made a seat reservation.
I wish you a great time in Switzerland. Should you have further queries, even while travelling, get back to us for assistance, we are gladly there for you.