Monthly €7.99 x 2 fees from APPLE.COM/BILL with no credit card associated to any Apple Account that I know of!

As far as I know, my VISA is not associated with any Apple account.

Still, I'm being charged two monthly €7.99 fees by my bank, with the description APPLE.COM/BILL iTUNES.COM.

Also, I have no purchasing history in my account (and besides... the VISA card associated to my account is not the one being charged!).

That is almost certainly evidence that your card/account number has been compromised and it being used by criminals posing as Apple. It happens with other retailers as well. We had bogus charges showing as a major chain store where we'd not done business since long before the advent of online shopping. That was a big clue.

If that is the case and Apple has no record, they did NOT make the charge to your account and cannot do anyting o fix it.

When we had this happen to us, our card issuer AMEX was aware of the scam and had everything sorted, including erasing the debt and issuing my wife a new card number, with 24 hours.

A senior contributor here found reference to this scam on a third-party web site:

https://toughnickel.com/scams-fraud/Apple-iTunes-866-712-7753-Scam

Apple has limited informatio here:

If you see 'apple.com/bill' on your billing statement - Apple Support

and I've asked Apple to contact me to figure out if this case is similar to the one you described.

Apple will not be able to help if scammers mase the charges. Only your financial institution/ card issue can fiox it.