Shocked by that requirement from CEX, it would completely reveal your identity.
CEX.io, like most centralized exchanges, demand invasive KYC from all their users. See the two links and quote below. It's pretty scummy that they would let OP deposit fiat and trade that fiat, and then only demand KYC when he tries to withdraw, essentially stealing his coins if he isn't willing to compromise his privacy, but they certainly aren't the only exchange to pull this crap.
https://cex.io/aml-kychttps://blog.cex.io/news/verification-requirements-17071We are obliged to make verification mandatory for all users.
As answered above, your coins are in your wallet once the transaction gets mined.
No, they aren't. The coins never leave the blockchain. The only thing stored in his wallet (or any other wallet, for that matter) are the relevant private keys.
I am guessing this could be Binance. They have a lot of policy when it comes to using card to purchase crypto. Don't know about other CEX.
OP is referring to the specific exchange CEX.io, not the generic term for centralized exchanges.