Suppose I want Esus as my state religion and I want to maximize its religious influence.
What's the chance that unit built in city with Esus religion will start with Esus promotion?
Also how can I get rid of other religions from cities? There are no Esus priests, hence no Inquisitors as well :(

For chance to start with Esus religion I think it depends on how many other religions there are in the city,

Although for a guarenteed unit with Esus religion try building the Esus only units such as Nightwatch,

For removing the other religions from a city.... well the only way I can think of is to use purge the unfaithful.