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As a replacement for "difficult," "hard" is casual. (1. & 2. - the meaning would be the same.)
Offhand I can't think of any situation where "hard" means "not easy" but can't be replaced by "difficult" with no change in meaning.
However, the converse is not always true. There are some cases where replacing "difficult" by "hard" might change the meaning or sound unnatural. An example that comes to mind is "a difficult man" (= "a man who is not easy to deal with"); "a hard man" means something rather different.