The Vilebloods are what I think the game's depiction of vampires, and Annalise is a blood queen, just like how Lost Children of Antiquity are depictions of gargoyles. Hunters are like Van Helsing, but I don't know, I just think it's a more simple way of describing things. There are quite a few depictions of vampires throughout the game, we just don't consume blood the same way.
The Vileblood are definitely "vampire-themed", and Cainhurst looking like the stereotypical Dracula castle is definitely no coincidence. The point is that inside the game universe they are not "vampires" any more than the people of Yharnam, who drink blood on the regular and defined their whole culture around it (we are told).
There's no evidence in the game that somebody can become a kin of the cosmos by consuming blood alone, but you can by Insight as confirmed by Willem, who looks to be turning into an Ebrietas kind of Great One by the looks of the growths on his back.
No, there isn't definitely proof of that, it was just me trying to make sense of the situation. Because, in reality, the only reason why you bring Blood Dregs to Annalise is that her backstory used to completely different, and that is a leftover of a VERY late rewriting of both her backstory and the overall game plot (which happened so late that parts of it survived in the 1.0 retail version of the game, and were only removed via the day-one patch).
We have an entire different set of unused recorded dialogues for her where she explains that she already gave birth to the child of a Great One, that is the reason why she can't die, and that she needs the Blood Dregs to reduce the "purity" of her blood and finally be able to die. Her child was meant to have been taken by Lawrence and used in some kind of ritual (1.0 description of the Third Cord form the Old Workshop), likely whatever brought the Hunter's Dream about.
But all of that was removed from the game, and Annalise was repurposed as a more evil character. The Blood Dregs part is probably just a leftover of that, and they didn't really bother to explain it in-depth other than "she wants to drink blood to become stronger".
I do know all these things, however the biggest mystery in the Chalice Dungeons is how all of the Great Ones we've fought exist down there, and there has to be a lore explanation for it but there isn't any in the items.
The Chalice Dungeons in the form they exist are never explained, and possibly can't be explained. They are 80% a gameplay feature and 20% lore-pertinent. They canonically exist, are located below Yharnam, can be accessed by people from the real world, Byrgenwerth found the Old Blood there and they sort of bend time and space when you traverse them.
They are there because From Software wanted them there. Just like you can't really explain what the fog walls are or why they exist, or how can you go and help somebody else in their game via the Small resonant bell. In Dark Souls the excuse was "Time is convoluted", here it's "Reality and dreams are being blurred by the Blood Moon". I'd leave it at that.
Ebrietas I completely forgot about, I was always under the impression that her blood was the Old Blood the church was describing. Alfred's dialog about blood healing may help, but the Choir may or may not have been responsible for the mass amounts of blood ministering.
And I always thought the Old Blood was blood of a Great One based on the "holy medium deep within the tomb", and the Isz Chalice is the last one I believe. It could be Ebrietas's blood or the Amgydala's as Amygdala's look more beastlike but, anyway, the Old Blood is what's responsible for breastbone, so if Annalise has been consuming it, she should have more beastlike features.
Alfred doesn't really know anything, he is just a low-level dude with a boner for the myth of Logarius.
The Great Isz Chalice description says:
Great chalices unlock deeper reaches of the labyrinth. The
Great Isz Chalice became the cornerstone of the Choir, the
elite delegation of the Healing Church.
It was also the first Great Chalice brought back to the
surface since the time of Byrgenwerth, and allowed the
Choir to have audience with Ebrietas.
Which means that anything to do with Isz and Ebrietas happened much later than whatever Byrgenwerth did originally when they found the Old Blood. Other items call Ebrietas the "left behind Old One", and say that the Choir are studying her to understand the cosmos.
Amygdala is a completely different story, and one that the game really doesn't explain at all. Going by cut/hidden content again we can infer that Amygdala is something Mensis discovered, and that the One Reborn is an attempt by Mensis to create another Amygdala (Amygdala is called "False God" in the game files, and One Reborn is "Incomplete False God" or something to that effect). But what is Amygdala exactly, or if it even is a singular being projected in different places or there are more of them is anyone's guess at this point.
Also, I don't think that the Old Blood transforms people in the sense you mean, with one blood making you one thing and another blood a different thing. The Old Blood acts as a general "trigger" for starting to transform in general, but the result of it seems dependant on completely different factors. Think of all the patients in the Research Hall, which existed at the same time as people in Yharnam randomly mutating into beast and requiring a stable force of Hunters being created in the city to keep the issue at bay.
The amount of Old Blood taken could, though, be connected to how "far" one will transform - which could explain why the members of the Clergy become massive lupine beasts, while common people usually range from this
to this
Ironic, Micolash was calling out to a dead Great One. How did Kos grant Rom's eyes if she's dead?
There's no evidence that Micolash is dead in Yhar'Gul. He could just be in limbo for all we know.
Micloash in the waking world by the time you meet him is literally called a "mummy" by the game, so I'm fairly certain he has been dead for a long time.
Also, this is just speculation, but wouldn't it make sense if most Great Ones were actually... dead, as far as we understand it from the point of view of the waking world? The game says the Great Ones went to "sleep" in the Chalice Dungeons at some point, but it doesn't sound like they might wake up at any point in time, and the Chalices are referred to as tombs in a few occasions. The only Old One we undisputedly meet in the "real world" is Ebrietas, and she is referred to as the "left behind Great One", is said to be crying (Rosmarinus description, in Japanese "maiden" is the same word then translated as "daughter" in "Daughter of the Cosmos") and spends all her time intently staring at Rom's corpse (Rom herself is debatable I guess, but I'd argue she doesn't exists in reality proper given where she is and how you reach her - and you find her "corpse" in Upper Cathedral anyway). Mergo and the Orphan are definitely dead, yet you meet them in the dreaming world. Micolash himself is dead in the waking world but still alive in the dream until you go and kill him there as well, so it's clear that being alive in one world has little bearing on your status in the other one.