Your train of thought seems a little bit scattered. I'll try and follow along as I respond.
- In order to prove the non-existence of a god, you have to rule out not only all possible places it could be, but all possible things it could be. The study of what something is is called ontology, and the ontology of even the Christian god is terribly vague.
- The idea that the real god might not be the Christian one is the best response to Pascal's Wager. Well done coming up with it yourself.
- There is no available physical evidence for any of the figures or events you mention, only documentation in the form of the Bible and some other writings. That's why these texts are defended so aggressively. They're the last and only line of defence for Christianity, and Judaism too.
- When the gospels were written is no more settled than who wrote the things. As the link explains, Christian scholars tend towards a range of dates in the middle of the first century (20-30 years after the apparent crucifixion), while others think it was closer to the end of that century (30-60 years after).
- The God is Imaginary website doesn't really prove that God is imaginary. It does have some very clever arguments which turn scripture against itself and portray certain beliefs as very silly indeed. It's become infamous enough that evangelists have posted direct responses. This guy has written fifty proofs God is real to counter the site's fifty "proofs" God is imaginary. Not one of his is a real proof either.
Amber, it might be a typo but I've never seen this use of the word "penny" before. From context I'm assuming that it means "inadequate".
What your mother says is true in a way. If a god exists and is truly omnipotent, then it can do anything it wants to: form the solar system in the wrong order, make it look billions of years older than it really is, give a man the power to cure blindness by touch, and bring the same man back from the dead. Such a being, hypothetically, can change or suspend the laws of physics to achieve its goals, and also manipulate or bypass whatever constant logical constraints the universe may have.
This can have varying effects on an argument, depending. It's basically useless to argue that an omnipotent god can't do something. The possibily that a god is omnipotent pretty much guarantees that a god is possible (since it could be hiding anywhere). However, that which is possible is not necessarily true.
If we conclude from research that the Bible's stories are illogical, then we would have to dismiss logic to believe them. That means we would need an entirely different reason to believe, or we wouldn't do such a thing. So what reasons do people have to believe in the Bible besides logic?
It may be an emotional reason, like simply wanting there to be a Heaven. It might be a default, since one's family might always have believed and one follows along by sheer trust. It might be because of apparent personal experience of God: while at a charismatic church someone is "taken by the Holy Spirit" and starts speaking in tongues. (I think this is a combination of over-enthusiasm and subtle hypnosis, but it certainly does happen.) Otherwise, maybe someone has a particularly convincing dream or hallucination of God. What the hell, maybe God really does exist and comes down to say hi to some lucky sod.
So think about the people you know, for example your mother. Why does she believe, if not because of logic? (Relating back to your other question, has she ever used a bible dictionary to sort out an apparent contradiction herself?). Most importantly (and this is the reply to her which I think you're looking for), why should you believe the stories in the absence of substantive evidence or logical support as far as you can tell?