Since Tor IPs are often banned as some users abuse them and try doing malicious stuff through them, Binance will most likely either ban your account or freeze your funds if you attempt hiding your IP through Tor as well.
Yup, and then they will request KYC to unlock your account. Every exchange which offers both KYC and non-KYC accounts has a plethora of complaints across every platform from here to reddit to social media of people having their non-KYC account locked for completely arbitrary or even unknown reasons, everything from "We don't like where you have deposited/withdrawn coins from/to" to "You logged in from a different IP than usual". Whenever you use an account a centralized exchange, you are at risk of being
asked to complete KYC locked out of your account and having your coins confiscated
unless you complete KYC.
You are never anonymous using a centralized exchange, your privacy is always at risk, and your KYC documents can be asked for at any time without notice. If you don't comply, say bye to your coins.