They went to a big supermarket downtown. It was noisy there.

(Q1: What is the part of speech of 'downtown' in Sentence 1? Is 'downtown' used as an adjective modifying 'supermarket'? Q2: what does 'It' refer to in Sentence 2?)

Yes, "downtown" is being used as an adjective to modify "supermarket."

"It" has no specific antecedent; it's referring to the general atmosphere in the supermarket.