Would half a syringe of Juvederm work for my smile lines? (Photo)

Yes, this will give subtle improvement to your smile lines. It will take 1-2 weeks for final results. Hope this helps. 

Yes, your lines aren't very deep and 0.5 mL would definitely soften the lines that you do have. Remember, you don't want to completely erase all lines (as it looks unnatural) but placing a little more filler in there can definitely help soften them! 

Half a syringe of the filler may not completely obliterate your smile lines but it will definitely help you soften them. Good luck from New York City

The product used on the under eye region is usually thinner than that required for the nose to mouth lines so I would be surprised if the product you have left over is suitable. I am also very cautious when preserving product as bacteria can get into the syringe and increase your risk of infection. 
If the product is thick enough then 0.5ml will improve the lines but may not be enough to completely address them 

Juvederm is a great filler. Because it causes more swelling, you can use less product, and get more visual change.Go do it!Best. Dr Brecht Seattle, Wa