Do you know what kind of figs you have Barbara? Are they green and stay green or turn purple?
The white (green) figs are probably kadotas. We have 3 trees in the backyard with more "volunteering" all the time. We probably remove 3 or 4 every year simply because they take up too much space.
Don't know how to keep the critters away because between squirrels, tree rats and the birds, it's every critter for hisself. That said, we pick ours every day when they're in season. And it's a short season, maybe 3-4 weeks, max. They don't keep very long at all so they're best eaten raw when they're very fresh.
I make preserves with mine (as a few of our friends here have sampled) and mix the figs with almost anything I can get my hands on as well as making straight fig preserves.
They go great with cheese or on lamb or on toast with butter. Also make great gifts. If you're interested, I'd be happy to share the recipe. It's so easy, even I can make 'em.