They were used correctly but the sentences were not quite natural. I just heard that Tom has been demoted for some reason. Actually, he seems to have a beef with his boss and his boss seems to have it in for him these days . Anyway, I think his boss should have it out with him if he really has a bone to pick with him. Why demote him instead? Note: - I agree that boss or supervisor sounds more natural. -Actually, I can tell that he seems to have a beef with his superior and his superior seems to have it in for him these days . // You should pick either "i can tell that" OR "he seems to have" not both. ex. I can tell that he has a beef with his supervisor. ex. He seems to have a beef with his supervisor. Having both is just repeating yourself.

I think that you used all of the idioms correctly for the most part. To make it more natural you should use boss instead of superior. For the last two sentences I'd probably say "If his boss really has a bone to pick with him, he should have spoken to him about it rather than demoting him.'