NOTHING can be "proved." The great hubris of naturalists is that empirical assertions are "proved" because they are supported by empirical observations. That is horseshit and doesn't get nearly the mockery it should. Empiricism is every bit as much faith based as the person sitting in the pew reciting "I believe in God the Father Almighty.... " etc.
The object of faith is different. That is the only difference.
Huh?
You either ignored or missed the quotes I put around the word 'prove'. It is the Creationists who demand that things be proved 100%, no scientist I know concludes that his work 'proves' anything. Your comment about empiricists is wrong, I doubt there are any strict empiricists in science, I suspect they are all pragmatists, but in any case the simple observation of an event or object is never taken as proof of something but as a start to investigation.
If you want to discuss requirements of 100% proof, talk to all those Creationists who demand Evolution be proved by direct observation. Scientists will just shrug your question off as coming from someone misinformed.
Just as a final note, you are equivocating with the word 'faith'. The 'faith' used by science is much different than the 'faith' used by the religious.