Proofs of God's existence and non-existence

Since the atheism thread got cluttered by repeated personal attacks I'm here opening a new thread devoted to discussing the core discussion that was made in that thread. Hopefully this thread will not degenerate into repeated personal attacks and accusations barely acceptable within the forum rules. If you want to do these things, I refer to the atheist thread, and please ask all who want to post in this thread to refrain from doing so if the post is a personal attack rather than an attack on arguments.

Basic debate subjects for the thread:
1. do you think there is any proof following the rules of logic that proves God's existence or non-existence? If so, which proof? Make clear which definitions you're using for "existence", "God" and other words whose meaning might not be entirely clear, including words that have standard definitions, since there might be small differences in meaning among different people. Beware that no logical proof of God has been shown yet, so if you want to claim to have logically proven the Judeo-Christian God's existence, I can recommend reading through the failed attempts known as "Ontological argument", "Cosmological argument" (including Kurt Gödel's formalization of the proof) and "Pantheistic argument", see wikipedia. Similarly nobody has been able to prove God's complete non-existence, but many properties of God have been logical contradictions towards each other and thus some definitions of God have been logically proven impossible, while however not being able to rule out the existence of a being with the other properties.
2. do you have informal arguments for God's existence or non-existence? To avoid confusion, please state in your posts whether you're presenting a formal or informal argument, since informal arguments aren't meant to be scrutinized by logic.
3. do you think logic is a good method to use for arguments for or against God's existence?
4. do you think religion is still religion if God's existence could be proven?
5. if you're atheist, would you if God's existence were to be proven, start believing in God?
6. if you're religious, would you if God's non-existence were to be proven, stop believing in God?
7. what is your opinion of Occam's razor in relation to belief in God?