Most, yes, but with plenty left over. They charge this for all transactions, whereas the wholesale/processing rate depends on the type of card. Pin debit transactions clear interchange well under 1%. Visa and mastercard have a few different tiers. There's not much margin in an American Express transaction at that rate, but your average VISA/Mastercard wholesale costs will net out to ~1.5%, depending on the kind of merchant you are and what kinds of cards your customers tend to use. (It's more expensive to process a reward card like the Chase Sapphire Reserve than your local credit union's visa card.) Square covers lots of different merchants, with special prominence in low denomination restaurants / cafes. At scale, that's pretty lucrative.
Yes, and scale eats directly into that rate. The Big Box Stores are paying pennies per swipe.
If that's true for credit cards, then they're losing massive amounts of money on cash back and rewards
The "issuing bank," which issues your cash back or rewards credit card, has its cut protected by the payment networks. Part of the "interchange," the wholesale cost of processing a payment, is reserved for paying out the issuing bank. The interchange rates are set for the payment processors by the card networks (Visa, Mastercard, Discover, Amex). Whether you spend $100 at the locally owned boutique or Costco, they get paid the same amount. The middleman— the payment processor— gets squeezed by merchants like Walmart and Costco, competing to shrink the margin for the promise of massive volume. But Chase, Captial One, etc. don't have their consumer credit card divisions affected by who processes the card. (Unless you're Citi's processing side with Costco, and only accept Visa. Then your competitors get zero volume from Costco on their mastercards, discovers, and amex cards)
They make it back from the smaller merchants that are paying the full 2.75%. Local stores need Visa a lot more than Visa needs any one of them, but when you get to the Walmarts of this world the dynamic is rather different; if Walmart stopped taking Visa it would hurt Visa almost as much as it hurt Walmart.