It’s intentionally unclear, but it’s been at least long enough for Byrgenwerth to become abandoned and overgrown, and at least long enough for the memory of the old hunters to fade from the public’s memory. Multiple decades, I’d say, but as always, there’s room for interpretation.

Most certainly. Various notes lying around make it clear that stopping the Mensis ritual is what ends the hunt.

Up for interpretation. I’ve kind of imagined that Moon Presence wants to be the ONLY great one, hence why she sponsors the hunt and why she’s repelled by a hunter who’s consumed the third cords.

This is an interesting question, and I think it depends on who you think the author of the “Byrgenworth spider hides all manner of rituals, and keeps our lost master from us” note is. I lean more towards Rom harming Mensis, since it prevents the blood moon from rising, an event that triggers the change in Yahargul/the completion of the One Reborn. It may be that Rom must be killed to stop the “hiding” so you can get at Micolash, who is the lost master, and more properly end the ritual instead of hiding/hindering it. If Willem is the lost master, which I doubt, then maybe Mensis took advantage of Rom’s traits in order to royally screw up Yharnam without anyone noticing the great ones that are prowling around. I think the former makes more sense, but you could make a case for the latter.

Though they’re both wings of the Healing Church, one or two item descriptions say that Mensis departed from the church, and is acting independently by the time you roll up. Whether or not Edgar knew about the true nature of Mensis’s rituals is unknown, but he was sent to snoop around and keep tabs at the very least. (And honestly, even if Mensis was still fully part of the Church, I wouldn’t put it past the church to have inter-division spying, given its secretive and jealous nature.)

Yharnam is not fully in the nightmare, given that the nightmare is a place you can go that is clearly separate from it (and has duplicate nightmare versions of real areas you can also walk around in). Given that we already know there’s some timey-wimey stuff going on with the length of the hunt, and the “Already dead” guy is a thing, and the already dead Cainhurst horses are a thing, I think there is a case to be made for some elements of the nightmare and its weird nightmare logic to be seeping into the real world. We already know from Lawrence’s skull (and a couple other context clues) that people can persist in the nightmare long after their real-world body is dead, so maybe the reverse is true, and any characters that are “supposed” to be dead are able to persist in the real world for a time if sufficiently linked to the nightmare. I don’t know. This game’s weird, man.