Q1.
Does the portion of the ball facing you appear to be illuminated or not?
Answer
At position E — the ball held out towards the lamp — the side facing you is not illuminated. You see a dark ball.
Why it happens: The lamp lights the far half of the ball, the half pointing away from your eye. The half turned towards you lies in the ball's own shadow. Your head is the Earth, the ball is the Moon and the lamp is the Sun, so this arrangement — Moon between Earth and Sun — is exactly new Moon day (Amavasya).