I have predictive shot lined up and for all the requirements for Optimized Prototype.

I roll three dice, two hits, one blank. I spend one hit to remove my opponent's shield (Optimized Prototype). Does my opponent (with 3 agility) roll one green die for the single remaining hit result? Or do they get two dice because I rolled two hit results?

only one die. you only have one result.

Card images for reference:

Although you pay for it when declaring your attack, the Predictive Shot only takes affect on your opponent "during the Roll Defense Dice step." And Optimized Prototype tells you to Spend a result, which is covered as a standard dice modification in the Rules Reference (1.0.3) p9.

Attack dice mods happen before defence dice are rolled (p5) so however many hits/crits you have when they roll green dice, that's how many dice they get to roll (in this case 1).

Predictive Shot limits the number of green rolls to the number of hits+crits in your attack pool "during the Roll Defense Dice step". The die you spent is already gone. They'd roll one die.