Yeah, VIC is an AI. The book says that there are "conflicting reports" as to whether the time travel actually happened, but here's my two cents: the time travel idea was first suggested by Sarge, and it's easy to dismiss what he says as the ramblings of a mad man. As for Church's time loop, you need to remember that the whole thing was run by Gamma, the deceitful thoughts of the Alpha. Gamma was used to deceive the Alpha before, so it's not a huge step to say that Church's time traveling was all simulation fabricated by Gamma.

Is that what Gamma is? The lies of Alpha? What about Sigma? What is he?

Sigma is the creativity. How much of RvB have you seen?