The concept of an orchiectomy is the removal of testis, so no, it's impossible.
Cutting the T production, uh... With prolonged HRT, maybe it dies down? I know fertility disappears, but I'm far from sure about hormone production.
Well, uhm, no, I don't think you can. You can block T's effects with anti-androgens, but not remove T itself if the testes are still there.