Absolutely. At frost/freeze in the fall, I pick everything bigger than a small marble so it doesn't go to waste.

You can but it will be sour, I think.
At the end of season I make pickle from green tomatoes. They make a much tastier and crunchier pickle than cukes. Add a few stalks of celery, some tomatillo ...carrots.

Thanks, Seeing how closely they are related to ground cherries and that unripe GCs are poisonous, I was worried about eating very immature tomatillos.