Will a non-volatile solute always lower the vapor pressure of the pure solvent in solution? Why or why not?

Answer 1

Yes, it will ALWAYS.
Why? Think Raoult's Law.
p = X*P^o and since X of the solvent will ALWAYS be lower than 1 (when mixed with the solute) so the partial pressure must always be lower than P^o, the normal vapor pressure of the pure solvent.