Cainhurst looks more like DLC material included in the main game, unrelated to the rest.

Prepare to hear sobbing for at least 10 minutes straight if you don't kill all the ghosts

What is that red rune looking thing that you get inside that castle, what I mean is when you are you the castle some of the monsters may summon a red thing on the back of your head. What is that and what does it do?

This Area would have been Perfect, Then they Dumped Screaming Ghosts everywhere Instead of putting Actual Enemies (and yeah, the Cainservent's, the Gargoyles, but those guys Pale in numbers compared to the MOTHER FLIPPING GHOSTS)

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Probably in the minority here, but Cainhurst was one of my least favorite areas. For an area this late in the game, most enemy designs here aren't as intimidating as the stuff in Byrgenworth or Old Yharnam. So many rooms are gauntlets of those stunning, shreiking, tanky lunatic women. And the number of cheap traps those gargoyles laid for me. Good lord...

This page states that Cainhurst is so far away from other locations that the blood moon doesn’t show up there but it also doesn’t show in old Yharnam either so it’s nothing to do with distance.

By the way the lantern doesn't show up right in the middle of the red carpet its kind of off to the left side of the room by some statues close to the red carpet but after you talk to the wueen and turn around then its on the right.

Another thing to consider: if you call the carriage while fighting (get too close to the obelisk) and, after the cutscene you DODGE to avoid the enemies, the carriage disappears. BUT - it wont be gone forever, just reload the area, and you'll find it right there, waiting near the obelisk. Got me angry for a minute, thought that for a stupid dodge i missed it in that playthrough.

The carriage will also despawn if you accidentally hit it while being attacked