a) More or less.
b) Your first sentence is basically the point.
c) Start with 1 in the top left corner. You now need to get 3 in the next black diagonal square - you have two ways of doing it. Then 5 in the next - another two ways. Then 7 in the next - two more ways. Then you need to go back and fill in the rest of that half before winding up with 17 in the bottom right, and you'll find that if you've chosen badly on the previous decisions you've made it impossible to do this.