but in this case the wallet's password( I think it's called private key)
Passwords and private keys are two very different things. In the case of interacting with an online exchange service, your password would allow you to log into you account on the exchange. That account would be associated with some collection of addresses that are provided to the user by the exchange. The private keys for those addresses would be generated and known by the exchange (but not the user).
would be in the exchange's hand and if a website hack or any other issues happen( even maybe the exchange decides to steal all the money's) we lose what do we have on their wallet. Is that correct?
Yes, when a third party controls the private keys for your funds, they will have unilateral control over those funds. You are at their mercy, if the worst case scenario happens to play out.
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