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Past isn't a verb. The past tense and past participle of the verb to pass is passed.
We can use past as a noun: Don't think of the past; an adjective: The past week was warm; a preposition: We walked past the church; an adverb: The train went past.
As is a conjunction, and is usually followed by a noun or pronoun in the nominative case. Like isn't a conjunction, but an adjective which behaves like a preposition being followed by a noun or pronoun in the objective case.
Fool is a noun, and requires the article when we use it with the verb to be. Foolish is an adjective, and can't be used with the article after the verb to be.
A fool or a foolish person doesn't mean an insane person, but one who acts thoughtlessly. We tend to use silly or stupid instead of foolish in modern usage.