If I've understood the 40K universe correctly, there isn't one unified church but rather a sprawling mass of churches, branches, orders, sects and cults. Some worship the Emperor as a monotheistic deity, while others dedicate themselves to some sort of aspect of him (usually death, right? ). Some churches seem to be moderate while others are flame-toting, pitch-fork wielding extremists. What decides which sect a schola progenium orphan ends up in? I guess most end up in the more moderate/conservative parts of the church, or can they more or less choose freely? Or is there an orthodox/catholic church all schola progenium joins?

The other imperial branches a progenium can join seem to be more or less uniform entities (the administratum, the IG, the arbites) but the clerics seem to be some sort of a wild card. I mean, the empire wouldn't want to invest all those resources in a child just to have it wander off and join the bat-**** crazy redemptionists or a minor cult on the fringe to heresy, right?

On a side-note: aren't there imperial assassin schools? Why isn't the assassin an option for schola progenium then? I can think of a few uses for a indoctrinated assassin loyal to the imperial ideals...

Scholas are run by the MInistorim directly, so they would take thier faith directly from Ophellia IV(can't remember if this is the correct current for the centre of the echlisarchy), most of the other itterations of the faith are bassicly to make it easier to allow new worlds to be brought into the Imperiams dogma easier, "so you tend to worship the sun, will the sun is the reperentation of the emporer so you don't worhsip the sun, you worship the emporer now get back to work", but major sector capitals and such will fall into the main line faith, at least thats what I take it to mean, so the Scholas will follow along that line.

As for assassins I don't see why you couldn't have an assassin from a schola because like you said they encourage beleif in the general rightness of the Imperium so it shoudn't be a problem to make an assassin from one but it would be something to discuss with who ever is running a particular game.

As stated above Schola Progenium isnt really meant for Assassins.

I guess you could argue that something like it exists for producing Vindicare Assassins fluff wise, but it doesnt really have a place in the game, as discussed to death, neither do the Vindicare except as something horrible to sic on the players at Ascension level...

The Assassin background packages in IH pretty much cover what you are looking for. They represent 3 nutty. "we stab/shoot things for the emperor and or money" groups.

Its important to remember that most of the Assassins presented in DH are some flavor or another of a death cult, with the obvious exception of the Sons of Dispater. Not all Assassins have to be death cultists though.

Assassination isn't legal in the Imperium. Assassins are criminals. Granted, they can be somewhat tolerated by the local governments (various "guilds") or quietly protected by the Inquisition or the Ecclesiarchy (various death cults), but officially, they're still heretics.

Schola Progenum teaches the best, most loyal, most faithful cadres the Imperium has to offer. No heretics, hence no assassins.

The only truly legal assassins are those fielded by the Officio, and Officio prefers to recruit from scum of the earth. Schola education would be wasted on Temple Assassins anyway.