I think the major exchanges now mostly require KYC but some have their limits set to at least a certain amount of BTC or any coin that you are using to be exchanged if you are non-KYC. I think it would be hard to have right now some exchange that supports Non-KYC. I think it's better to use P2P instead.
That is correct; if you use CEX, you should anticipate that there is a KYC. However, with certain of them, KYC is not required and you can withdraw a small funds. I don't believe so if a centralized exchange does not recommend or does not have a KYC component on their platform. Because it is centralized, they should provide a KYC. KYC was designed to prevent fraudulent activities. If you want to withdraw funds to your bank, P2P is much better because there is no fee, especially if you use Binance, although KYC is required to access this option.