On Metamask there is wallet general address starting with 0x. Is this the address Binance asking from me? Is there other specific address of Wing on Metamask that I should use?
Yes it's the address that you should use it. Wing token is EVM token, which is also supporting BSC20 binance smart blockchain too. Just use it, and there's nothing to feel worry about.
It's one address that can be used in various blockchain.