So a big question we've had come up is: Can you fate or spend fate to boost your requisition rolls?

I haven't been able to find anything in the rulebook on this, and so it seems that you can indeed spend fate points to improve or reroll your requisition check.

However, we sometimes use requisition checks as a kind of reward for a job well done after a session (or before next session starts), and for those checks we don't allow spending fate.

I'd suggest only doing requisition rolls at the end of session*. If a player has fate points remaining, then let them spend them. If you don't want that happening, it's up to the GM to make sure players spend all the fate points during the session. Which I've seen happen in sessions with no combat or any risk of injury to PCs.

*If they aren't at a location where they can receive the goods, have the goods go to their home base and stay there until the players pick them up.

In Dark Heresy 2E Influence is considered a characteristic and thus you can you fate points to reroll it as you can any other one.