Continual revision is a key part of the scientific method, so of course science doesn't claim exactness. The only thing science can "prove" is a negative. As far as everything else goes, we can only say a model is consistent with all evidence thus far collected. If today someone proved a negative by demonstrating the incorrectness of a model science has championed for years, they would not be viewed as a heretic, but embraced and given a Nobel prize.

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... and that is where their hypocrisy comes into play. They claim to be able to explain everything through scientific procedure and experimentation

Most scientists do not claim that they can explain everything. If you find one who does, he's probably not a very good one.

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Yet, historically speaking, all of science has begun with just that - a thought or faith that someone endeavored to prove correct.

Is there something wrong with having a hunch that a relationship exists and then seeking to validate your hunch through experimentation?

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Life is a mystery. Science is trying to explain, not solve, many of those mysteries ... but for what purpose?

It sounds like you're in agreement with Einstein here. In Science and Religion, he spoke about science and purpose. Science in a vacuum is purposeless, and it is something outside of science that drives the questions and what to do with the answers. For example, our values might motivate us to develop a cure for cancer. Science can help with developing that cure. But after it's developed, what then? Science can't decide how much the pharmaceutical company should be able to charge, or if the uninsured should or should not be denied the cure due to not being able to pay.