Duo gave me the sentence a second time, and it does accept "He pulls, pushes, and it closes well." I didn't take a risk on "tight."
For Duo sentences, I either imagine a children's book with big pictures and one sentence per page (e.g. "The bear eats a fish") or a murder mystery (e.g. this sentence, where the detective is obviously sneaking into someone's house.) :-)
Objects have gender, therefore you would refer to "it" as "lui" or "lei"
"Literary subject pronouns also have a distinction between animate (egli, ella) and inanimate (esso, essa) antecedents, although this is lost in colloquial usage, where lui, lei and loro are used for animate subjects as well as objects, while no specific pronoun is employed for inanimate subjects."