1 - Taking as "squares" only the individual ones and not the composed ones, and understanding that the white ones are not counted:

2 - Due to how the fractal iterates, the shortest path for the ant is always the same: going straight to any corner of the central square that from his POV is placed transversally, and then to the opposite corner.

For example, if the ant starts in the lower left corner, it must go straight to the lower right corner of the central square, then to the opposite corner. That path is safe for all iterations of the fractal, and always the shortest.