The first is that, no, they can't directly trace your public key if you send ethereum as most exchanges have multiple wallets at least. Binance seems to have at least 3 for example.
Well, yes, they have the actual public specific key used since they can see the address of sender on etherscan. Even if exchanges have several keys, at least in my case, the same keys has always been used to withdraw my ETH and to deposit to the receiver i sent it to. Was i just unlucky they used the very same key all the time? or is it normal? If so, as i mentionned, it becomes "fairly easy" (even if it must be extremely tedious) to trace the transaction back to the user even if the public key is extremely active. indeed, just a few transactions separated enough from one another in time to narrow it down to locate the same public key that is always withdrawn from every time receiver gets ETH.
Third, try not to send the same amount in and out of exchanges if you can help it (or similar) sending 0.987 btc into an exchange and withdrawing 0.9865 is going to make it fairly easy for someone to think both are from the same person regardless of anything else.
But we have to. When we send a certain amount to someone's wallet via our exchange, he'll receive that exact certain amount all the time. So, he'll know. And the exchange will always take that exact amount from the same public key all the time too.