An apple with is refrigerated stays fresh for 2 weeks one thats not refrigerated would be 1 weeks.
Maybe about a week and an half, but if you just leave it out maybe about 2 days or less
It depends upon the type of apple but it will start the spoiling /rotting process as soon as it is plucked.
Two weeks
1 week and a half
About 1 week
A few weeks probably