The paradoxplaza redeem pages states that:

"You will receive redeem codes if you buy our games outside Steam or our own store. These codes allow you to unlock private game-specific forums as well as forum icons."

Where can I find those?

The serial key should be in your web gog profile. Click on the game in your shelve. Then click on More and on Serial keys. I haven't it there on launch but it appear there few days ago.

But I solved it by contacting Paradox support, so I don't know if these serial keys are the ones who are redeemable on Paradox.

The codes are only available if you log into the GOG main page, Galaxy won't show them.

The Battletech/Battletech Deluxe Edition code need to be entered on the Paradox website once you are logged into your Paradox account.

The Shadow Hawk Bonus Skin Code needs to be entered in-game, under account management.

It's rather unintuitive and I wish the whole process was explained somewhere else, but here you go.