Firstly, unripe figs WILL NOT ripen off the tree. DON'T pick them unripe. You'll notice I said "unripe", not "green". Also, once ripe, figs spoil very quickly. Refrigeration will slow it somewhat, but most people thing it also ruins the "fresh" taste of figs straight from the tree. IF you've never had figs on this tree before, you're not going to be able to go on color alone. It could be green, yellow, blue, brown, or striped when ripe! The thing to watch for is the figs will start to droop and soften a bit when they approach being ripe. Some will wrinkle considerably. If you have a lot of figs, watch for the first to droop, and pick one. If it doesn't seem ripe, let the next stay on a little longer. Continue letting subsequent ones stay on longer, until you're satisfied that you have a ripe one. THEN you'll know what color fig you have, and how long to leave them on the tree. Hope this helps.

If the branch is complety off then remove all the figs and most if not all the leaves so it will concentrate all the energy into rooting. If you have rooting hormone apply it to the branch and put in soil. Keep the branch in shade or inside for several weeks. Cover the tear in the branch in fungicide to keep fungus from attacking it. Figs are survivors and it will live. Do you have a picture?

Unlike most trees, it does not hurt to plant fig trees an inch or 2 below the soil surface. The part that is planted below will just sprout more roots. Most trees do not do this and suffer disease and may be killed. And yes, if you regularly irrigate your entire yard (more than 1 inch of surface water) it could cause the "bathtub effect". However, since I use to live in west Texas and by the look of the pictures, I am assuming you are not regularly irrigating your yard. If you are watering to keep the yard alive, it will not be enough water to cause the bathtub effect. If it were mine I would amend the soil in a 4 foot area to cover the root ball and mulch on top of that. I had a fig tree in a dry area with clay and it did not grow much at all for 4 or 5 years. I finally mulched it with about 3 to 4 inches of pine bark and added a little fertilizer last year and It grew and even made figs. Do not fertilize too much or it will go vegetative and grow but not produce.

Yes ,they do produce smaller fruits when young. If in pot ,it matters how many fruits you let grow,if too many formed,then the young little ones need to be taken out,to help tree ripen the rest. It takes about 80 to 90 days of Summer to ripe the fruits ,counting from when you notice them.