My bad, didn't read properly. Gotta say though, a lot of questions like these can be easily answered by a quick look at the laws of badminton >.> http://www.internationalbadminton.org/page.aspx?id=10513 Again, I'd assume it'd be a close call (and more often than not be called a fault) unless you swung at it quite a while after the bird hit.
I don't think there needs to be much of an interval in the case of a drop shot as it's already going downwards. The key part is "starts to fall towards the surface of the court", in a drop shot as soon as it hits the net it's falling.
It's also no longer in play soon as it hits the net. Anything after that happens after that is moot. I think it'd be a close call unless you have someone judging from the sidelines; especially if you're playing with someone who isn't very good with the honor system >.>
Not always, if you're at the front and lift and it hits the net on the way up then it's still moving upwards so you don't know which side of the net it's going to land on therefore it's still in play. Happens with a hard smash as well when you hit the very top of the tape and the shuttle moves upwards before moving down again.
I guess I deserve a response like that for not being specific enough, but in the situation being discussed it's assumed that it didn't clear the net >.>