1) this is not the way people normally use the word "proof" in relating to science. They generally mean a logical proof similar to what is used in mathematics.
I doubt this very much. The average person talking about a scientific proof doesn't know anything about mathematics, either, and so how could they be thinking of mathematical proofs?
Namely, scientific theories must be amenable to DISproof (they must be disprovable in principle), but are never provable in the same sense.
No, of course not. But many scientific explanations become so well-tested that only crackpots dispute them. And certainly statistics gives us the power to conclude that a certain result is not simply due to chance; and moreover, to assess what level of confidence we can have in that conclusion.
I think, when most people talk about "proof", they're talking about observations that can only be most reasonably explained by the conjecture in question being true, and that's certainly a standard science can meet. Proving things by logical transformations from assumed premises isn't something a majority of people have experience doing, and so I doubt very much that's what they're thinking of when they say "proof."
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