Hello!
"Quickly" is an adverb since it is describing the verb, "sped."
It answers the question "how did it speed?" - It sped <em>quickly</em>.
The second one, the last one ( I think )
She asked what I was doing when I knocked at the door.
Answer:
Proctor believes that Abigail accused Elizabeth of witchcraft because Abigail wanted revenge on Proctor for rejecting her. When Elizabeth says to Proctor: "The judge sits in your heart judging you", it means Proctor: carries the knowledge of his own guilt in his heart.