How many days and nights does the action require in Othello?
There is a bit of a jump in the narrative of an undisclosed portion of time. The play opens of course one night with Iago and Roderigo outside the house of Brabantio, whom they rouse with the news that his daughter has eloped with Othello. Later on that same night, Othello both faces his father-in-law and also his rulers, who send him to Cyprus straight away to fight on their behalf:
At nine in the morning here we'll meet again.
Othello, leave some officer behind
And he shall our commission bring to you,
And such things else of quality and respect
As doth import you.
Thus a few hours after the end of Act I, Othello leaves Venice for an undisclosed amount of time as he travels to Cyprus and wins his rather lucky military victory. This is the jump in the narrative. The action picks up again at the beginning of Act II, with the rest of the play unfolding over the next day. Thus it is impossble to authoratively answer your question because of the jump in the narrative between the end of Act I and the beginning of Act II.