We do need to go through the requests to pull your coins to make sure your account is in good standing to do so, but it would not be a long wait (under a day maximum)

We will not rehypothecate your coins, you always have a key to verify that is the case. There are even third party services you can use to notify you if your coins move on the blockchain, and we encourage you do to whatever makes you comfortable with the setup. The coins will never move.