why is there a shadw in the center of the circle of the light from a flaslight?

Answer 1

Because the parabolic reflector behind the bulb does not have a reflective surface at its center since that is where the bulb resides. However, just because the center of your spot light is darker doesn't mean that there is no light at that spot, it's probably still brighter than the area outside of that which you are illuminating.

The geometry of the bulb itself also plays a role in this. Often times you will have a bulb shaped similar to a christmas tree light sort of like this: ()
The glass that makes up the outside of the bulb acts like a lens and redirects light according to it's shape (try removing the reflector and shine the bulb close to a surface to see what I mean). A spherical bulb is likely to have less of a dark spot at the center since the light from the filament spreads evenly in almost all directions.

Note: some flashlights have an adjustable lens assembly that can narrow the output beam sufficiently to compensate for this dark spot.

Answer 2

It's where the bulb is and no light from the reflector goes there.

Answer 3

It's due to a central minima. Interference - i think... jus guessing