If you want to.
Do you sketch with a light pencil first?
Other than the obvious "Press more lightly with the stick," you can also blend using your fingers, a cotton ball or a soft rag.
What options are there for making gradients and blending shadows?
You can erase charcoal with a kneaded eraser.
How do you deal with mistakes that ruin a piece?
They sell fixative specifically for this purpose. It comes in spray cans. You can buy it any art-supply store.
How do you prevent the coal from rubbing off when finished? I tried hairspray and it doesn't work well.
Because the graphite makes the surface of the paper slick. Yes, you should use charcoal pencils instead of graphite.
Why doesn't the coal stick to areas that have been colored in by pencil? Am i supposed to be using coal based pencils instead of graphite?
Be more thoughtful and judicious about the marks you put down. If you lay down thick heavy areas of black, they are going to be difficult to erase.
How are you supposed to use an eraser when it gets completely black within 10 minutes.
Find a reference photo that approximates the view you're attempting to draw. Compare, contrast, and correct your drawing until it looks right.
Also some critique of the piece itself would be helpful. Is it because the neck is badly shaded and off axis, or is it a focal point issue? Also, it looks too cartoony - i assume that's from the anatomy deviating too much from realistic human ranges. Are the nose and jawline the worst offenders in this case, or maybe its the brow area?