Faith and logic are capable of coexisting, but they are not complementary. Faith is the decision to consider something true without a logical basis, and sometimes inspite of a logical contradiction. The decision to have faith is made not because one has discovered a logical deduction of the claim, but rather because one has been convinced through some other means, such as emotional motivation, trickery, or ignorance. The belief in the existence of God, for instance, is usually justified by arguments such as: it makes the believer a better person; it's comforting to the believer; it's hard to imagine any other way the universe came to be. These are not logical arguments for the existence of "God". They are logical arguments for the choice to acknowledge the existence of "God". This is fine for people who are willing to sacrifice a little sanity to gain happiness, but I consider evidence of truth to be the only acceptable justification for belief.

I agree. A purpose behind the existence of the universe and humankind is essentially what the concept of "God" is. I find those interpretations of "God" being the Big Bang, or even the universe itself, to be a bit of a stretch on the concept. At that point, they are not purpose driven, ... they are not even evidently capable of thought, so how do they suit the role of God at all? Sure, they're cosmic and all, but "God" is a lot more than that. Personally, I would sooner claim the non-existence of "God", instead of handing that label off to the nearest hard-to-conceive phenomenon.

There's a distinction that should be made with the word "purpose". Do you mean the purpose "God" had in mind when creating us, or the purpose that drives humans through life? I think that those who want to serve "God" want to make his purpose their own, and thus they blend the concepts together without realizing it. Those who believe a "God" exists may be searching for the reason/purpose behind the creation, but those who are agnostic on the issue don't bother. Everyone either has a purpose, or is looking for a purpose, but not everyone is looking to "God" to provide one. Searching for purpose has nothing to do with faith, unless you're talking about having faith in the existence of a divine purpose.

One cannot explore while settled in one spot. To resign oneself into having faith that "God" exists is to avoid exploration for many possible reasons, e.g. comfort, ease (simplifies your life. no need to think critically), etc.

An analogy: Let's say there's a tornado coming towards me. I can simply calm myself and say "Oh, it'll turn before it hits my house." Afterall, why would I want to believe that it was going to hit my house? That's such a bleak possibility. Unfortunately, my comforting beliefs do not change what will really happen. If it indeed does hit my house, I will likely die because instead of preparing, I was comforting myself.