I really haven't noticed mine getting stringy/tough until you start being able to see the seed outlines (not at shelly stage but moving toward it). I usually pick mine when they're a bit bigger than yours in the picture. Maybe try letting some get to different stages and then test them to see what size you like best.

Yes. I gauge them by the beans bulging out. But younger = more tender. Taste them at different stages and pick your preference. Rattlesnakes, I usually pick with a little bean bulging.

The size they are at now is perfect for snacking on while in the garden. For cooking with I agree with the others that they can be left to get larger without any decrease in quality.

Rodney