많-아 is conjugated form from 많다. 많다 means to be a large number of or a large amount of. 많이 is a derivative of 많다.

많아 is an adjective/descriptive verb. It's usually found at the end of the sentence e.g. 사람이 많아 (there are many people) 많이 is an adverb, so a verb/adjective has to follow. E.g. 많이 했어 (I/you did a lot)

많아(요) is the conjugated form of the descriptive verb (adjective) 많다. 많이 is the adverb form.