Question #1
Continuing its upward climb, the gasoline TODAY gained more than ten cents per gallon.

What part of speech is the word TODAY?

adjective, adverb, noun, preposition, pronoun, or verb?

(I say adverb because it "gained" today)

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She knows that TO PASS THE TEST she must read thoroughly

What part of speech is the grouping of words "TO PASS THE TEST"?

dependent clause, independent clause, prepositional phrase, main clause, verbal phrase,

I believe it is NOT an independent clause or the main clause, but I'm not sure about the others.

1: adverb (adverb of time qualifying 'gained').

2: verbal phrase.