Trim Path effect

There are direction to paths! Who knew! If you are manually doing drawing the path in AI, follow the direction that you want the animation to work.

Now, for the this piece here I would put a solid on top. Use the pen tool to draw line that follows the your shape (middle not around) and then drop a stroke effect on it. You can then animate that to your liking. There is a way to do this with the path you have but the answer is off the top of my head

EDIT: Here is more of what I am talking about. Drop a shape layer, grab your pen tool. And mask around your shape. and then animate the points. The amount of points will determined by your animating style

Also set the lay that you are masking to track matte the layer that is animating the mask.