Now is the time to step up and study.

On my infinitive is it the whole phrase to step up and study? And am I correct to say an adverb

The phrase is correct. It's an adjective phrase modifying time.

Yes, you are correct. The infinitive phrase in the sentence is "to step up and study." It functions as a noun phrase in this sentence, serving as the subject of the sentence. As for whether it is an adverb, the infinitive phrase is not acting as an adverb in this particular sentence. It is functioning as a noun phrase, indicating the action or concept of stepping up and studying.

Yes, you are correct. The whole phrase "to step up and study" is an infinitive phrase, where "to" is the infinitive marker and "step up and study" functions as the infinitive verb phrase. In this case, the phrase describes the action that should be taken, emphasizing the need to take action and dedicate oneself to studying. It serves as an adverbial phrase because it modifies the verb "is" by providing additional information about the timing and purpose of stepping up and studying.