Many arguments purport to prove the existence of "God". Here are a few.
Those arguments are valid. The premises are questionable but not absurd. Problems show up only before and after the kinds of arguments isolated here.
The main reason to prove the existence of God is to justify a religion. The main problem with these proofs is that "God" is a slippery word with inconsistent meaning. Justifying a religion requires that you prove the existence of not just any "God", but a powerful entity which cares about the actions of humans in a way largely (but not exactly) aligned with common intuitive morality. Justifying any particular religion introduces more constraints (usually many, weirdly specific constraints) on the traits of that "God".
The arguments given above correctly prove that there are things that could reasonably be called "God". Respectively:
Atheists sometimes like to apply Occam's Razor to God, saying that they have no need of that hypothesis. A less drastic application, more valid in light of these "proofs", reminds us that the "God"s introduced in the proofs are most likely the simplest entities fulfilling their role in the proof, and need not have other traits. To prove that there is a powerful entity caring about human actions, one needs further evidence that the entity under concern cares about human actions. Abstract entities concluded from common proofs do not justify any religions.
Juxtaposing the proofs given here doesn't even prove that the creator of the universe is maximally good, or that the creator of the universe also created life, sith there is no evidence — not from just those proofs, at least — that the target of each proof is the same thing. People only think otherwise by sloppily equating the inconsistently-reused word "God".
There exists God, just not at all the God people are supposed to care about.