1. Yes, I've always had to use my passport with my Eurail passes; though often it's to prove I'm an American who is eligible for the cheaper pass.
2. No, only in certain countries. I've bought SIMs from vending machines in Iceland and Denmark. In Italy the merchant made me seriously promise, I really mean it to send him a photo of my passport as soon as I returned home with my SIM. He gave me his personal gmail address to do so (probably because he certainly didn't want that info going to his work email where it would be obvious he ignored the rules). In Germany, rumor was you basically had to be a German citizen to get a SIM; that turned out to be untrue but I cannot remember if I gave them my (EU but not German) passport. IIRC I could not buy a SIM in Sweden as a non-resident though. UK was no problem to buy a SIM.
3. Yeah, but that's just an identifier. You could use any number, and a different number for every merchant, and nobody would know. Though there was a case of a fireman convicted of arson, partially on evidence of firestarters bought using his wife's Safeway loyalty card number.
4. I can't really ever remember being asked for my passport in the 5 of those 6 countries, but of course it's not unreasonable to be expected to show ID so I cannot say for sure I never produced ID. Though I remember in Poland and I think the Czech Republic they actually hold your passport, which made me very uncomfortable. When you leave the room for the day you swap key for passport, and vice versa on your return. Whether this is government or business policy, I do not know.