There are no actual vampire clans as printed in the module and supporting material. What you have are two factions within the entirety of Ustalavic vampire culture that either support the Whispering Tyrant's return or oppose it. Of the two, the supporters are more rare since the Tyrant's return would usher in a world where the vampires would have no food supply (since the endgame is everyone alive being dead). That being said, in my game I utilized the old World of Darkness type of clans to parallel some of the unique personalities that are presented within the module. I don't know if you played Vampire (I assume you have since you're referring to vampire clans), but I broke it down as follows:
-Ludvick: Ventrue
-Merrick: Gangrel
-Lady Evgenya: Toreador
-Arkminos: Nosferatu
-Radvir: Brujah
-Aisa: Tremere
I had Desmond Kote be a villain and had a nest of Urgathoan worshipping vampires (Sabbat) lurk in the darkest catacombs as a red herring for the true vampire murderer. Some of the changes I used can be found in my Expanding Caliphas thread and my review of Ashes at Dawn here. Hope some of that helps.
As to your questions-
1 and 2)I assume its one vampire per 100 people in the city, including Spawn. For its 15,640 people, this makes about 156, give or take (which is substantial). You can divide that number among the most prevalent vampires to come to a number for each clan, with fluctuations based on the vampire's personal preferences with regard to spawn, feeding, and so forth.
3) As written, the conflict is between those that want the Tyrant back and those that don't. As expanded, you can certainly have the different personalities and their retainers clash on political and martial levels. For my part, I had spawn corresponding to different vampire "clans" have different powers, such as Merrick's spawn having a barkskin ability to harden their hide.
4)To a degree like any hierarchy, they all answer to Ludvick, but from there, I imagine each individual vampire has its own lesser network of spawn and servants. There are of course exceptions, but since Ludvick is the oldest and most powerful among them, he has all the cards.
5) From all that is written in Rule of Fear (an excellent supplement), Caliphas in mentioned as a city where vampires roam. I imagine in mechanical terms, it would reduce the percentage of vampires in those cities versus Caliphas to somewhere between 1 in 200 to 1 in 1000 people being a vampire.
Since it's relevant to the topic of this discussion, I suggest that you check out Lords of the Night by Dreamscarred Press, assuming of course that you haven't already.
Part of its focus is a vampire-only campaign, but I think there's plenty of material in there for the vampires in Caliphas. It also contains a sample group of vampires - the Leatherworkers Guild.
I intend to utilize it and the various Occult books quite extensively when I revisit Caliphas.
If you want to break it down into individual clans, I would have them each headed by the various NPCs presented within the module itself. This would be as follows:
Ludvick: The leader of all vampire kind within Caliphas, possibly one of the oldest things still existing within the Inner Sea Region. His rivals are few except those that want to either revive the Whispering Tyrant (Malyas, see Shadows of Gallowspire) or break free from Ludvick's control (Radvir). His servants include his stand-in Florian, and a number of sorcerers, and fighters, and anything else powerful you feel is appropriate. He probably has the most actual vampires and the fewest spawn. Probable vampire number: 31
Merrick: Her ties to nature present almost a hunter-like aspect to her and her minions. In this regard, some of her minions would probably be classed vampires with Ranger, Slayer, or Druid levels beyond her spawn. Her spawn lost their energy drain attack, instead gaining two claw attacks and a +2 bonus to natural armor. Her clan is responsible for occasionally culling undesirables from society and guarding the way to the Vampire Court. Probable Vampire number: 18
Lady Engenya: From her description, it seems that she favors the most charismatic members of society, stealing away some with simple Aristocrat levels, but also some with Bard and Sorcerer levels. I had her spawn lose their natural armor but gain Ability Focus: Dominate as a bonus feat. She and her clan would be those responsible for influencing mortal affairs within Caliphas.
Desmond Kote: This would be the religious sect of your vampires, with the majority of the vampires allied with Kote possessing cleric, warpriest, and inquisitor levels. While fewest in number due to the non-dominance of religion among vampires, the power of their followers insures that their house is one to be feared. His few spawn possessed the Advanced template. He and his followers are responsible for maintaining order within vampire society. (This is different from my game) Probable Vampire Number: 12
Radvir Giovani This would be your commercial interest for the vampires, with Radvir and his associates using their power and wealth to operate or front numerous businesses throughout the city. I imagaine a lot of this wealth makes its way back to Ludvick, but a good chunk is probably used by Radvir to eventually help try and stage his plan. His vampire minions besides those written would be rogues and bards. Additionally, I'd check the Ashes at Dawn GM thread for some excellent additional minions. Probable Vampire Number 22
Slain Vampire Mother of Quinley (an others) This could have been someone responsible for delivering messages throughout Caliphas, diplomatic liasons with other supernatural entities, or travel to and from the city. Quinley's mother (and any others) could have had fighters, rogues, wizards, oracles, or anything else that seems appropriate for the deceased. Probale vampire number: 14 and 30 various vampires between two other slain leaders.
Hope that helps!