Oh, gosh. I did not realize that I am showing up so late. Anyways, here's my two cents.
1. It is not based on proof. This means that if you can prove what you believe in, you don't have any faith.
I think you are making a simple logical error. Even if:
Proof => Faith
Does not mean that:
Faith = Proof
I suggest a better description of the relationship is:
Proof + Believe => Faith
2. What about if there's no evidence at all... is that faith? Believing in something with absolutely no evidence, is what I would define as stupidity, and therefore not faith.
You suggest that
Proof + Evidence + Faith= Stupidity
Infants must take a great deal of their interactions with the world on faith, because they do not have the context to make sense of their world. This starts to diminish at age three, when they learn the magical word, “Why?” and begin to ask about our blue sky.
Infants aren’t stupid. They are marvellously adaptive. They continue to believe that their supper will arrive until evidence suggests otherwise.
3. What about if there's evidence, but it's not conclusive? This seems to be a good definition... so if there's any kind of evidence, and that evidence makes you anywhere between 0.00001% sure, or 99.99999% sure then you have faith? Well this conflicts with "being SURE of what we hope for...", because being sure, means being 100% sure.
Nearly every interaction with the world requires a certain degree of faith. There is nothing we can be 100% sure about in this world. Quantum mechanics blows away all the apparent certainty and materiality , yet we continue to believe that a struck key on the keyboard will give the same result.
So perhaps our certainty can never be 100%
...
5. ...In order to solve my problem with understanding faith, I used to define it as having enough evidence that you act on that evidence. For example, if you are 1% sure that Jesus exists, and you are baptised because of it, then you have acted in faith, and therefore you have faith in Jesus. Of course this conflicts both with the bible definition and #4 above.
But what if faith is not evidence based? I’ll use analogies outside of the biblical realm. We have two sides of our brain; one which is delegated the logical functions, and the other that manages unstructured, three dimensional information. It is this other side of the brain that makes shape and sense of our world, and allows us to distinguish a wife from a hat.
As an artist, I’ve worked hard to exercise this other half of my brain. I paint beautiful pictures. Some of the lessons learned as I’ve worked through this process I cannot express, and when I do, I ruin it. These paintings come out of that other, inexpressible part of me.

Why is it ruined when I try to explain it? Because I cannot deconstruct the process into logical, binary steps. (01001001001000000110110001101111011101100110010100100000011110010110111101110101).
Another concern about the definition of faith is that it is personal. This means that evidence in favour of what a person believes is usually accepted, and evidence against is rejected. I believe that this can also be defined as closed-mindedness, or stupidity.
Based on my description above, such a faith MUST be personal. The stupidity perhaps may come from thinking that this personal faith is self-evident and that others who have not experienced it, are false.
Presuming that faith could be open-minded and unbiased, would mean that it is the most likely outcome of evidence which has been thoroughly investigated and tested by intelligent, open-minded individuals. Obviously that is not faith... that is science.
At this point I think you are making too many leaps. I have challenged that faith is NOT logical, and cannot be properly deconstructed using the logical model. It still is useful, allowing us to move through our world with a certain degree of certainty.
I might mention also that the english word, “faith” may be too broad for use. We use it for complete trust and confidence in anything, not just belief in a set of religious doctrines.