Suckers: I am leaving the ones on my tree alone until the tree goes dormant. Then I will dig around them trying to preserve as many roots as I can, cut them off, and pot them up. Since we have milder winter temperatures, the roots will grow and establish themselves while the top stays dormant. Next spring they will be ready to grow.
Air-Layers: I've not tried to layer a limb with fruit on it. It *should* be okay since a girdle (yes, I normally girdle my air-layers) only disrupting the flow of nutrients to the parent tree and not to the limb.
I also have an alternative to doing the air-layer this weekend which maybe safer and you won't lose too much time... Instead of air-layering, wet the limb where you would normally be doing the layer. Then wrap with black electrical tape (sticky part out). Like this:
If the weather is still hot and the leaves do not provide enough shade, wrap a piece of foil around the tape to keep it cool. Then wait for the transformation to happen... let say about 4-6 weeks or after your figs are ripe. Remove the electrical tape. You should have some adventitious root nodes forming along the limb where your tape was. It should looks something like this:
and like this:
and like this:
Once you remove the tape, put on a your air-layer media as usual. The roots will grow quickly from these nodes.
If one prefers to air-layer in the spring, I *THINK* (some experimentation is needed) will work while the tree is dormant. This will give the layer a head start in the spring. The new tree will have more time to establish itself before the onset of summer heat.