I want some hints in how to solve these questions:
How can I separate two different point by polynomial in the coordinate ring $\ k[X] $?
Edit: Concerning 1: If $b$ and $c$ are integers, then $b^2+15c^2$ is non-negative, so it can never be -2 or -5. If $c>0$ then $b^2+15c^2\geq 15$. If $c=0$ then $b^2+15c^2=b^2$ is a square number and thus cannot be 2 or 5 either.