Tree? Don't know - Our black fig gave us a few the following year. But much must depend on age?
Have never seen a green fig advertised - hence the great pleasure.
Cook? NEVER! Just as they come, & you have to be quick - they over ripen in a couple of days.
If I did have to preserve them, I would probably bottle them in a weak syrup.
PS That's Yoghurt, not Cream!!