Suggested answer:
(1) The corpus returns two different words starting in "hard", viz. hard and hardly:
Looking across the valley to the scars of North Hush, it seemed hard to believe that these deep gouges in the earth were manmade...
... it seemed hardly likely that I would get into any serious trouble.
(2) In the example with hard we have a complex sentence starting off with an Adverbial clause Looking across the valley to the scars of North Hush. Then we have an empty it functioning as an anticipating Subject followed by the Verb seemed and the Subject Predicative, realised by the adjective hard. The real Subject then follows to believe that these deep gouges....
In the example with hardly we also find it functioning as an empty Subject, anticipating the real Subject that I would get into any serious trouble. While hard was seen to be an adjective functioning as a Subject Predicative, hardly serves another function altogether. It is an adverb premodifying the adjective likely. Together hardly likely function as the Subject Predicative.
As to the meaning difference between the two expressions with hard and hardly: while hard has the meaning of "difficult", hardly has the meaning of "not at all".
(3) Example of hard as an adverb:
Again he had to think hard.
(4) The sentence is grammatically incorrect because the adverb intended here is hard ("energetically") and not hardly ("almost not" / "barely"). If the latter was intended, the rest of the sentence does not make sense either.
Internet Grammar of English
Terminology: adjective, adverb, subject, subject predicative, anticipatory it, premodifier
* Quotation taken from Stewart Clark's Broken English Spoken Perfectly, Frifant Forlag, 2004.
