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Three photos beat one: the whole tree, the bark up close, and a branch. Leaf shape alone is ambiguous. Leaf plus bark plus branching usually is not.
Sometimes. Shagbark hickory is unmistakable; most young bark is not. Send it anyway — the answer tells you how sure it is.
Genus nearly always, species most of the time. Cultivars and hybrids are the hard cases, and it says so instead of guessing.