"Please close the door slowly."
Shouldn't it be ドアを not ドアは? Or is a different rule when there's an adverb coming after the noun?
I've been told that ドアは would be more general like "please close doors slowly," not specifically "that door."
"When it comes to doors (/the door), please close them slowly". There's nothing strange about using "wa" here.
は is a topic marker, so I guess in this case it makes it obvious that it's the subject of the sentence.
We need more context. If someone is giving you a direct command, yes. Use "wo." If they're just talking in general, "wa" would also be acceptable.
Would it be acceptable to put ゆっくり at the start of the sentence instead?