Of course it's possible. Go to the Distribute tab in your game's control panel, and you'll be able to create download keys, that you can hand out elsewhere.
Yes, you can mark the keys as having to be claimed before people can download the game. That counts as a purchase, and makes it so nobody else can use the same key anymore.
No, I mean, how I know that the person purchased the game on Steam, so I can distribute the keys automatically for them. Something like with that .CSV file system of Kickstarter.
I don't know anything about selling on steam but I bet you could put a menu option in your game that ties in with the Steam API and requests an itch key from your own server.
