You should be given a transaction id. If that doesn’t show in the explorer, the Tx has not (yet) been sent to the network. I know from other exchanges, that they sometimes wait for several people to do a withdraw. In that way, they can bundle all the UTxO together in one Tx and save on the fees.
Please consider using a HW wallet, if you don’t already.
A beginner question about staking is answered here.
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