Hamza's first ability affects only generic mana costs. It can't reduce the total cost to cast the spell below {G}{W}.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Hamza, Guardian of Arashin). The total cost is locked in before any costs are paid. The mana value of the spell is determined only by its mana cost, no matter what the total cost to cast the spell was.

Once you announce you're casting a creature spell, no player may take actions until the spell has been paid for. Notably, opponents can't try to change the number of creatures you control with +1/+1 counters.