If you collapse and stop breathing, how long does it take until your fingers turn blue? or your lips go blue?

About 2 minutes: There's oxygen there until the person actually collapses; the tissues use the oxygen which changes the color of the blood and makes things look "blue". It's easiest to see in the fingers and lips, but actually occurs everywhere. When it's really bad, the whole body turns blue. Scary stuff! the cure, obviously, is to get oxygen moving in and out of the lungs again.