How long to cook green onions relative to other vegetables
I typically chop up the white and green parts of the green onion, and add them at different times during cooking:

I'll add the white part fairly early in the cooking.  (not as early as I would with bulb onions, as I cut the green onions more finely).  I want them to cook for a minute or two to take out the harshest flavors, but not cook too much.  I generally add them a minute or so before I add the rice to cook.

After I've cooked the rice for a bit, I'll add the green part.  This lets it soften up just a bit, but not really cook down.