She quickly changed her wig before the cops arrived.
He answered the question quickly and accurately.
Rapidly or speedy.
He did that equation very quickly.
Let's ford this creek quickly.
"Fastly" is not a word. The appropriate word to use in place would be quickly."She is doing it quickly" or "She is doing it fast" are both acceptable.
The birds quickly took flight.
Jim quickly took a snapshot of the table.
"The army had to mobilise its forces quickly, once word came of the impending attack."
The pickpocket quickly filched the man's cell phone.
We won't use that brand of paint again, the siding is weathering much too quickly.
Your answer would be: "immediate", "immediately", "promptly", "instantly". They're synonyms, so use whichever word you choose.
The cat is very agile. It can move quickly and in a precise manner.