Sometimes a problem has many parts, each of which depends on the previous part. If you can't get one of the parts, write how you would figure out the next part if you knew the previous answer. You should get good partial credit for this. The only time this is a good idea is if it is required to keep you awake for late night studying. If you're used to it, you can do it, but you'll never know how much more efficient you could be if you learned to study in silence.
Fewer distractions mean greater potential for efficiency.
This is a massive waste of time for some people. Learn to do it neatly the first time. For technical courses, a pencil and a good eraser do the trick. If the assignment must be in pen, do your best and use white-out where necessary. A little neatness is a small sacrifice for the time savings.