Besides being set in Cairo 1798 what is the main theme of The Blood Oath?

There are several main themes.

Number one. No one knows who the vampires are. Vampires from the outside have no idea who the local vampires are or anything about them. The reverse is also true of the indigenous vamps and the vamps from the outside. They don't know who is a vampire or not. This will be taken care of fairly quickly in some cases and much slower in other cases.
Vampires will be determined by random drawing after everyone has made up a mortal character.

Number two. The Blood Bond. Who is bound to whom at the onset? Who will be bound to whom by the third event? How will vampires treat these ghouls? Will your ghouls rebel against their masters? Can they? Will others help them to escape?
The Cainites will then choose their ghouls and future progeny from the remaining players. The objective is to make the players feel the the Bond. Some masters will treat their ghouls well, others will not.

Number Three. The indigenous vampires are mostly Setite and Assamite. They are not part of the Camarilla and now the French Toreador have arrived. Blood will be in the streets but the presence of the vampires must not be discovered. The Masquerade will be very important.

Influence
What is influence? Is it physical mortal pawns or is it a persons reputation in a given area?
Influence is a characters reputation/control over a given area of mortal concern.

If Influences is based on a characters reputation can it be stolen and how long does it last?
Yes. Influence can be stolen if their identity can be stolen (certain Disciplines make this rather easy)and the particular Inflence Traits have been identified. However, the theft is only temporary for that expenditure.

How do you identify a characters particular influence traits?
All influence expenditures can be tracked and investigated.

If we can spend influence to gain rumors, can we spend influence to spread them or is spreading them free?
It can be either, starting them without spending Influence makes the rumors fairly easy to determine their validity. Rumors started by spending influence are harder to reveal.

Can we set up influence blocks for everyone or do we have to specify who we are blocking?
I call this "throwing up a defense" yes you can do this. The influence is considered spent so once designated to defend it can not be used for something else if you change your mind during the event.

What Influence does the city militia or guard fall under if there is no Police Influence?
The guard/militia are controlled by Political Influence. For this reason I am allowing Politics to be used like Police Influence. In addition I am allowing Church to do this simply because the Church has a great deal of influence over the militia and guard just because they don't want to get into trouble with the Church.

Animal Ghouls

Is there a way to have an animal ghoul without having Animalism?
No. Animals who drink vampiric blood start killing everything around them until they are dead. They go into a frenzy that eventually will kill them. The character having Animalism helps the animal stay in control.