A valid Swiss Half Fare Card is not needed to buy tickets. During ticket purchase, the system will not check if you are entitled to buy tickets at a reduced fare - this is the task of the ticket inspector. Therefore, the Swiss Half Fare Card must be valid the day when you use the public transport system for the first time; hence, in your case, 22 June.
Unless you want to buy Saver offers, there is no reason to buy train tickets two months in advance, no Swiss resident does that. There is no financial benefit when you buy regular tickets in advance. In fact, it is the opposite: when buying tickets in advance, you will sacrifice flexibility as you can’t change plans at the last minute in case of bad weather when you already hold the train tickets. Yes, buying tickets ahead of time for mountain trips is risky. If the weather is poor, you won’t get any views. Far better to buy them on the day you go up, not to waste your money.
Generally speaking, public transport in Switzerland is mass transit, like subways elsewhere. Meaning, you get to the station, you buy your ticket, you look for the next train departure, you get on the train, and you enjoy the ride.
Swiss trains use free seating, except for some Panoramic trains (PE). Seat reservations are possible on Intercity (IC) trains only. Buying a ticket in advance will not guarantee you a free seat. You simply take a free seat on board the train.