Don't they bind addresses to your account? So when with deposit eth and trade for something else and come back at some point to sell something for eth then you get that eth back.
Not usually. Yes, each account has its own deposit address. In good exchanges, that deposit address will either automatically change after every use, or you will have the option to request a new deposit address, so you never have to use the same address twice, which is good for privacy reasons. However, most exchanges periodically sweep the funds from every user's deposit address in to a main, central wallet, and then pay out withdrawals from there. Leaving coins in each individual user's address would either leave them with huge amounts of dust, or leave them having to take coins from other users to pay a large withdrawal. So no, you don't usually get back the exact same coins which you deposited.
If you just deposit and not trade won't they just send it back using the same address you just sent it to?
The answer is still probably not. Although that might be cheaper and make more sense, most exchanges deposits and withdrawals are automated and don't have somebody making decisions at the other end. Simply put, you deposit to the address they give you, all deposit addresses are swept to a main wallet, and the main wallet pays out any withdrawals. Even if you try to withdraw exactly what you just deposited, the likelihood is the automated system would still perform as above.
I think it is best if you go from one currency to another and either keep that or trade that currency back to a second exchange and withdraw from there?
Changing currency isn't the stumbling factor to using an exchange for privacy. The stumbling factor is the exchange, and anyone working there or anyone they share data with, can see exactly what you've done. It doesn't matter it you deposit BTC and withdraw BTC, or deposit BTC, trade to ETH, withdraw some as ETH, trade the rest to XMR, and withdraw the rest as XMR. The exchange can still link all your activity, all your addresses, and all your coins.