In the US what happens is the card company says to Bob's Hardware, you must accept all our cards or you can't accept any cards, and our "Premium Reward" card has 7% interchange fee so when Jimmy presents his "Premium Reward" card for a $1000 purchase, the card company takes $70 of that. Jimmy gets $50 and he think he's a genius for having this card. The hardware store needs to raise prices for all customers to allow for people like Jimmy. So when Sarah, whose crappy job barely is enough to live on buys a product that would be $500 the store charges $540. Sarah's card only has an interchange fee of $10 and Sarah gets none of that, but the shop owner is legally prohibited from charging Jimmy more than Sarah and they're legally prohibited from refusing Jimmy's card unless they also refuse Sarah's.
Uhm technically yes, but functionally no.
When gas was routinely $3.5/gal in SoCAL (where I live), credit price used to be $3.5/gal and cash price $3.4/gal.
My credit card gives me straight 5.2% cash back on purchases at the pump.
I hence pay $3.3/gal - still less than the cash price of $3.4/gal.
No, they are desperate to pretend they've shored up a failing business model, and so they must constantly lure in more potential victims. You are temporarily subsidized by these schemes, but don't come crying to us when you end up behind the curve in confusing and changing credit terms.
I agree with your claims about busy work and hamster wheels.