Will help as much as I can. Others may have more details.
1.) Most of the larger train stations have luggage storage, but are really only used "by the hour." I stayed in Milano for 2 days before my flight out from there....and I went on the Bernina Express for a one night trip.
I left most of my luggage at my hotel in Milan and took a day pack. I took the train from Milano Centrale to Torino....then walked 20 yards to board the Bernina Express.
The train trip was beautiful. I went in June 2015 and the glaciers & snow were great! Considering, you can be in 85 degree Italy in the morning and within a couple hours be freezing in Alp Grum on the BE.
Plan your trip, though. Make sure you have activities.
I left at 9am on day one and made it to Pontresina about 1pm. It's a sleepy little town with not many english speakers. In the summer, it's fairly dead. I visited some of the local bars, the ONE market in town and generally just enjoyed the small town.
Hindsight, I would had planned some activities, like the Diavolezza gondola. Seeing some of the glaciers or doing some hikes. I just basically did it a whim at the end of my 2 week italy vacation...so I didn't really research it a lot.
The train ride is really nice. Definitely the highlight. I bought the 1st class ticket, but 2nd class would be equally great.
Also...the next day, I took the regional train back to Tirano. On the regional train, you can hop off at the stops and be OK. The Bernina Express train, you buy a ticket for your stop. You don't hop off at the stop.