1: Why do stores need to identify customers?
Stores want to cater to their customers. The easier they make it for you to find what you want in the store, means more money for them, and greater convenience for you.
Part of that effort is building a profile (age, address, etc) on customers, so they can guess what kind of products you'd like most in the future, and where to place them. It also allows them to send you customized ads that induce you to buy.
Note that in the old days when people shopped nearby, this same profiling was done by the store proprietor, who knew you and your family very well. Today's mobile buyers and temp employees makes this much harder to happen.
(This whole recent purchase privacy fad is silly. Most of us belong to store and card award programs precisely because we want custom deals. More importantly, we appreciate being noticed and catered to. That's why we go to the same stores and the same restaurants. When I go into my car dealer, I expect to get a better deal because they know me. When I go into my favorite eatery, it's nice to hear "Hi Mr. Darling! We'll give you your favorite seat and food!" When I go to the pharmacy, I like that the pharmacist makes special exceptions for our family and speeds things up. Only kids and crooks want to be anonymous, IMO.)
2: What justification do banks have to sell that information? Do banking regulations even allow that?
The banks themselves can't do it. But... the key is in the fine print of that privacy letter you get each year from your banks. It states that unless you opt out, they can share info with their close partners. Well, guess what kind of companies those are.
They don't sell detailed info to the merchants. That would diminish its value. (This is the same reason that merchants don't sell your info, either. It's more valuable if kept secret. So all the worries about that are bogus.)
Instead, they do like Apple does with iAds, or Google with Google Ads... they sell anonymous targeted ad spots. They'll also send out targeted coupons, and if that coupon gets used at a store, the merchant has to pay $1.50 to $5.00 to the bank. That can add up.
First I hear. To my knowledge the banks agreed to Apple's terms because Apple Pay reduces fraud (due to the biometric authentication), which reduces the banks' costs.
If you only hang on Apple sites, it's understandable that you think that. Try joining electronic payment industry sites as well, to get a better background on what's actually going on, what the banks really think, and what they had to agree to with Apple (such as giving back information on purchase categories and other statistics).
As for fraud savings, what Apple charges is more than what contactless fraud costs. In the UK, twenty times as much. Even in Australia, it's about five times as much, IIRC. That's one reason why the UK, Canadian and Australian banks balked at paying what Apple wanted, along with Apple wanting formerly proprietary data.
Remember, banks make money
because of fraud. The risk they take approving a purchase is exactly why they're able to charge such high fees and make such high profits. If there was no risk, the fees would be questioned (which is already beginning to happen in Congress).
Not to mention that Apple is only able to charge because they only allow NFC to be used by themselves. That grates on the banks too, because if they could use NFC and TouchId in their app, they'd have no reason to pay Apple. Apple is basically holding the banks' customers hostage.