My question is:
Is there any crypto to fiat exchange (no matter new/old, trusted/ or not, regulated/ unregulated and etc.) or market which accepts bank card payments and doesnt require ID verification?
An exchange site that accepts bank card payments that I don't know of, but for an exchange site that doesnt require ID verification, you can try Binance. So far I have been using their site for quite sometime now and they have not required me to send them a copy of my id's. With a lot of fraudsters around, I don't think there is an exchange site that accepts bank card payment and ID's not required. They also have to protect their business.
This guy wants to buy crypto for fiat without ID. Not crypto to crypto trading. Binance plans to launch this but not yet.
I would try to find someone on
https://localbitcoins.com - its service where you buy coins from users - even for cash.