Travel from Italy to Lauterbrunnen

Hello hipiper, and welcome! As for your questions:

1) You can either pre-order a 50% discounted train ticket through the SBB website, or purchase it at the border station (from where the Swiss Half Fare Card is valid) along the way. The first Swiss railway station is, in most cases, Brig. You often have to get off here anyway to change trains, but if you don't have a lot of time for getting in the next one, you may find that it's more convenient to already have your ticket. I'm not sure if it's possible to purchase your entire ticket at one of the larger Italian railway stations (meaning a ticket Florence/Venice-Interlaken, with a 50% discount for the Swiss leg). It's best to contact the Italian railways to find out. By the way, it doesn't make that much of a difference whether you travel from Venice or from Florence. In fact, faster connections are available from Florence than from Venice. The Swiss timetable shows all possible connections for both alternatives.

2) As far as I know, fares for trains running between Milano (in Italy) and Brig (in Switzerland) don't change as rapidly as they do for the TGV. Rates are more or less fixed, and pre-booking doesn't really lower the costs. You don't have to own or order your Swiss Half Fare Card yet when booking online; simply pick the 50% rate for the Swiss leg. As long as you have both your Swiss Half Fare Card and your 50% discounted ticket once you enter Switzerland, it's alright.

3) Making seat reservations for international trains (in this case, the train crossing the Italian-Swiss border) is often obligatory, so you can't really avoid this (unless you'll cross the border in a slower, regional train). Such reservations can often be made shortly in advance as well, so you may arrange for this during your stay in Italy, once you have determined on which date you want to travel to Switzerland. Your preferred seats may be not be available anymore in that case.

4) I'm not quite sure if Swiss or Italians trains are used, but that doesn't make a difference for booking the tickets. Generally the SBB website offers more possibilities than Trenitalia. The problem may be that a Swiss leg is involved in the journey, and that Trenitalia allows you to buy tickets and reserve seats for Italian trips only. In your case, it would be best to get to the SBB.

Does this clear things up for you?