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.