Hi sez77, mostly coach, sometimes public transport. However your Tour Leader will arrange tickets, usually obtain a few for each person. For the Discover Winter Tour, you’ll use the train getting into Rome city from where you get dropped off from the coach, so part tour coach, part train. Beware of pick pockets, especially on trains. Wear your backpack on your front or use straps to secure it to yourself. Prague, trams possibly, depends on your accomm location.
In Switzerland - if you do the Jungfrau trip (highly recommended!) the only way is up via mountain train, which is about 180CHF. A return ticket to the top, stopping along the way for a number of lookouts, take a camera .
I had a couple of cards (one travel, the other debit/credit card) and withdraw cash as I needed it. Most countries are on the Euro, except for Switzerland, Hungary, Czech Republic (Czechia).
Hope this helps!