Artificial gravity by spinning?

mfb

For constant angular velocity ω, g-force is proportional to the radius r: ##a=\omega^2 r##
Your "height" difference would be like a steep mountain, and air would be very thin at the small end.

The Coriolis force will give some deviation from a straight line - but you should reduce the "height" difference to get nicely flowing rivers.

"Down", towards the larger end.
Not the difference, the actual acceleration does this.
If you manage to get wind in some way, maybe. Otherwise, the whole air will follow the rotation of the cylinder without significant effects.
Only if you run at the velocity of the structure (as seen from outside), which is not likely for such a big cylinder. You would fall downwards, with some sidewards motion if the height is so large that it will kill you anyway (this happens on earth, too - for a free fall of ~100m, the deflection is of the order of 1cm if I remember correctly).
This is true on the inside, too. See my first paragraph how g-force changes with height.

k!rl

In regards to question 4, if the building is sufficiently high and the cillinder sufficiently wide, meaby air resistance or drag could slow you down so much that you'd lose your speed and thus your "weight" before hitting the ground?

Especially when using wings, wich should function normally as far as I can tell, so long as there is air resistance.

Sound like an interesting story already nalan, inspired by icarus perhaps. Interesting questions too!

mfb

Air is dragged along with the cylinder. Air drag will make sure you end at the outer border of the cylinder.