Hi marilou,
>> My family & I are traveling to Le Prese … in May … Pontresina … back & forth along the Bernina Pass … Val Poschiavo … Bernina Diavolezza … the Morteratsch glacier … Saint Moritz. What means of transportation do we take and any Swiss pass that we will need?
As rockoyster mentioned, the Swiss Timetable will tell you how to get anywhere. In your case, you will probably be mostly using regional trains along the Bernina Express line, perhaps supplemented by local buses and Postbuses depending on time of day and starting/finishing points for any particular trip.
The cable car to Diavolezza is not covered at all by the Swiss Travel Pass, but if you stay more than one night at a participating hotel, they will give you a pass for free transport on the local railways, buses, cable cars and funiculars. Participating hotels include budget hotels.
There is more information about the free mountain transport pass here:
http://www.engadin.stmoritz.c h/sommer/en/bergbahnen -inclusive/
However, with the exception of the Diavolezza cable car, most of the mountain transport in the St Moritz area does not operate in May.
If the restaurant at Alp Grüm railway station is open, that is a lovely place to stop off for views and refreshments. It usually reopens on the 2nd Saturday in May after a one-month break, so might be open when you are there, depending on your exact dates.
>> we will stay in Lugano for 2 nights, traveling via Maloja Pass & Chivenna … I need help sorting out the means of transportation that we will use.
This is the Palm Express PostBus route, which runs from St Moritz to Lugano. In May, it runs on Fridays, Saturdays and Sundays, departing from outside St Moritz railway station at 12:20. It is covered in full by the Swiss Travel Pass. Reservations are compulsory and free, and can be made here:
http://www.postauto.ch/en/exc ursion-tips/palm-express
Alpenrose