None of which have any influence on the core religious belief (read: statements on the existence of God) within a theological system. That is at the base of all religion and not subject to logic under any religion which claims a supernatural object. And if you can't prove the actual core with logic, then questioning the following ideas within that framework using logic only becomes possible if you take the core idea as an axiom. Meaning you can get to any damn conclusion you like via the insertion of your religions version of "GODDIDIT", but you can never rule out any conclusion for precisely the same reason. On the other hand, if you don't take the core as axiomatic, you have to make all your arguments from outside the framework. Which can and does address those claims, but falls flat against any argument made from within the framework once that damn unjustified axiom is invoked.
In essence, you can't make the argument for belief using sound logic because you can't get a testable premise. You can have valid logic in this case (since validity is only dependant on the consistency of the reasoning and conclusion, not the truth of the premises you're working from) but you can't have sound logic because the axioms remain unproven. Which means any conclusions you derive from those axioms will always be suspect even if they are the result of valid logic sequences.
The flipside to this is that you can't disprove the idea of God, only individual claims about Godhood. Even then, it's often rather tricky and generally best accomplished by attacking the internal consistency of the claim rather than the individual actions therein.
I hope that gives a more solid idea of what I'm trying to say here.
Course, the Bible is a good example here. You can't disprove it externally from the believers POV (God is axiomatic there and thus trumps a lack of evidence even when that lack is in places where there bloody well should be evidence. Exodus and the Deluge are the big ones there.) but you can demonstrate its internal inconsistency quite easily (frex, the fact that at least one story of Jesus birth is incorrect. Herod died in 4BCE and Judea couldn't have been subjected to a Roman census prior to 6CE, when it actually became a part of the roman empire. Therefore, at minimum, either the Matthew or Luke Gospel must be incorrect in it's telling of Jesus' childhood. Then there's the 2 different genealogies given in Luke and Matthew, both of which are different to the line of David given in 1Chronicles). The fact that its overall narrative has more holes than a whores fishnets helps, but it's hardly unique in that manner.
edit: Sorry for the jumpy structure. I'm tired and preoccupied with developing a new fiction story. I think I've cleaned the post up to a readable state now.