I think part of the problem is the inconsistency of Tolkien's own writing about the Ring - in The Hobbit, when he didn't yet know the ring was The Ring, it seems very handwavey "it's magic" just like you'd expect in a children's book. The deeper explanations came later.

I think enough of the wearer remains in this dimension that sex would definitely be possible. They're still physically present - they can eat (and steal food, keys, gold cups, etc.), they can be hurt or killed (or knocked unconscious for a whole battle) or hurt or kill someone or something else, they still make sounds and give off scent (that a dragon can smell even if he can't identify it). I don't really see any problems with having sex, assuming one's partner can cope with the sheer weirdness.

I think in the case of Nazgûl-blowing, it's probably better not to have a Ring - maybe you don't want to be able to see what you're doing.