In English, an adverb is a word that modifies a verb or adjective.
As an example of modifying an adjective: "He was very tired."
He - noun (subject)
was - verb
very - adverb (modifying 'tired')
tired - adjective (specifically a predicate adjective
As an example of modifying a verb: "Danielle quickly ran to the corner."
Danielle - noun (subject)
quickly - adverb (modifying 'ran')
to - preposition
the - definite article
corner - noun (the object of the preposition in this case)
So to borrow from your first instance: "His murders were clearly terrorism."
His - possessive pronoun
murders - noun (subject)
were - verb
clearly - adverb (modifying 'were')
terrorism - predicate nominative, a special use case for nouns (not an adverb)
The easiest way to identify an adverb is to ask what the word modifies. If it modifies a noun (a blue sweater, where blue is describing the sweater), it's an adjective. If it modifies an adjective (a very blue sweater) or a verb (a sweater permanently dyed blue), it's an adverb. (One can often identify verb-modifying adverbs by looking for the suffix -ly: quick -> quickly, intelligent -> intelligently.) Though the constructions of the latter sentences are more complex, none of those examples you cite are actually adverbs: they are all adjectives in some form. Terror, terrorist, and terrorism are all nouns. There is actually no adverbal form of terrorism that I'm aware of. The closest I can think of is "terrifyingly".