1) False
An anion is a negative ion. When an atom loses valence electrons (i.e. loses negative charge) it becomes a positive ion (called cation, not anion).
2) True
Non metals are at the right side of the periodic table. Those elements tipically have more than four valence electrons (except C which has 4 valence electrons). Then, by gaining some electrons (the number depends on the number of valence electrons that the non metal has), they can complete the 8 valence electrons configuration of the nobles gases.