Last minute 1st time EU trip this wknd and confused about Swiss rail pass, town to stay

1) Stay in Lauterbrunnen, Grindelwald, Wengen or Mürren, not in Interlaken.
2) They all have souvenir shops, restaurants, grocery shops. The most in Grindelwald which is the largest.
3) Without doing the arithmetic, probably the half price card.
4) Correct, See pass validity map here: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich_en.pdf

5) Yes, all towns accessable by rail. Wengen and Mürren are only accessable by rail / cable car, or on foot, no roads.
See map here: http://shop.hallwag.com/upload/files/HKF/04_JungfrauRegion_RS.jpg
Or for a better perspective (bad pun), map here (red is railways, black cable cars): http://cs9.pikabu.ru/post_img/big/2016/09/19/7/1474281363171890416.jpg

If you get the half price card, and the accompany childrens pass, for your trip from Milan, you will need to pay full fare from Milan to the border (Domodossola) and half price from there to your final destination.

Thank you for your reply. May I ask why you suggest not staying in Interlaken?

I like the idea of staying in Lauterbrunnen or Grindelwald. My only concern is how remote these towns are compare to Interlaken? Do they get quiet/dark at night early with no souvenir shops open (I'm guessing because the town might be more residential local area than Interlaken)?
We arrive in Switzerland (Interlaken area) on May 31 afternoon and hope to go ride the Jungfrau train on June 1. Some sightseeing on June 2 before heading to Zurich.
Does Lauterbrunnen have more things to see than Interlaken? Do they have cheese factory/shops nearby?

From your description, I'd say Lauterbrunnen would fit the bill. I assume 2 adults and 3 kids. There are some small mom and pop cheese making spots in Muerren where you can see it go from cow to cheese (not all at once of course) and buy of expensive but delicious cheese. From Lauterbrunnen it is an easy trip up to Muerren and also the Jungfraujoch on the other side of the valley. Make sure the weather is good the day you go or it might be an expensive disappointment. Get the free Family Card when you buy either the Swiss Travel Pass or Half Fare Cards for the adults, then the kids travel with you free.
If you get the Swiss Travel Pass, you get to Wengen for free and then adults pay 50% the rest of the way to the Jungfraujoch. With the Half Fare card, adults pay 50% for everything. The Half Fare card is good for 30 days only, but if if it saves you money (and if you go to the Jungfraujoch, it definitely will), it is usually the best deal. Have some warm clothes and jackets to go to the Jungfraujoch.

Edit, don't worry about finding places to spend your money in any of these. You'll find plenty. as they are all tourist central. But going to Muerren and Jungfraujoch, Lauterbrunnen is much better than Interlaken. It will save time visiting the spots you want to see, as well as money traveling with a Half fare card. They are in mountains rather than near the mountains.

tryatomy, all these places are primarily tourist destinations. Other than that there is a small amount of agriculture.
They all have restaurants open in the evening. Mürren is the smallest (population of just 450, but has 2,000 hotel beds).

Interlaken is a lot larger (population 5,692), in a wide valley between two lakes Hence the name - see map posted previously).
Lauterbrunnen, Grindelwald, Wengen and Mürren are further into the high mountains, in narrow valleys or perched halfway up the side. They are generally considered to be a lot more spectacular to stay there instead of commuting from Interlaken.

I suggest you do a Google images search for Lauterbrunnen, or for the other places.

Lauterbrunnen is about 20 minutes from Interlaken via train. Lauterbrunnen, Grindelwald, Wengen, Murren are all SPECTACULAR - Interlaken is not.