The web wallet is on a different fork, so simply sending coins from there to the QT Wallet will not work.
Here is a guide on how to import your web wallet private key into the latest version of the QT Wallet:
https://forum.bitbay.market/t/how-to-import-your-bitbay-web-wallet-private-key-into-the-bitbay-qt-wallet/2227
The QT uses only one key. The markets client uses two. However the web wallet uses compressed key format and markets wallet uses uncompressed. So until the web wallet is fixed I think there is no other way to use the two keys. We might add compatibility to markets wallet if time allows. However we update the web wallet anyways.
Yeah I realize that, we are working on updating the web wallet. If you are really in need to spend it before hand let me know and I can assist you. Meanwhile just wait a little bit for us to update the web wallet as we are working on it.
I don't know but it could be up to a month or two. It might be sooner but I don't want to give any expectations. Just be a little patient and check back with us. We have been busy. I just started going over it today actually.