I'm with Dan on this. If it is hot and/or dry in your area right now is not a good time to remove these because environmental stress will make the transplant much harder on the new tree.
As far as how close to cut, get as much root as you can with the new plant, but not so close you damage the mother plant.
Figs are like tomatoes in that they will root any where along the stem if covered with soil.
In the Summer and Fall, I often just bury low lying branches with dirt, or pin them down with a small U shape of wire if necessary, cover well with dirt, and then separate them out in the early Spring for transplant. If you have hard winters in your area maybe you might want to separate them out for transplant to pots in late Fall.
When it is this hot, it is good for ripening and picking figs but nothing else.
Best wishes to all.
John