Yes!

Yes, that is okay. I would personally say "an hour free" or "a free hour". If you say "one hour free" you are emphasizing that the duration is one hour. Also it would be a tiny bit more natural to say "you could" instead of "you can". If you say "you could", that emphasizes that it is your suggestion. Both "you can" and "you could" still sound good though.

It’s not too natural or clear without context. If you’re free after school, come join our chess club. (I think that you’re free and want you to join) If you have a free hour immediately after school, why not join our chess club? (I know that you’re free and want you to join) Anyone who is free immediately after school can join the chess club. (Stating a possibility with no assumptions or desires) Chess club lasts one hour immediately after school. (Needing to be free to participate is obvious) ‘Our’ indicates that the club belongs to a certain group that I’m part of. It’s ok but more common in my experience would be ‘the’ or no article at all.