It is a fig. It is very difficult to discover the variety, and possibly it has not variety. From such photos, I cannot tell you if figs will be much larger, or the colour (yellow or brownish).
Harvesting date: this do not depend on species or variety, but on your tree. When the figs become yellow or brownish, just touch them. It they are soft, take it and eat it. Experience will tell you what it is the best period for you (which possibly it will be different from your wife). In such manner, you will have fresh figs for weeks, and a lot better then on markets.
Note: I'm assuming you are harvesting figs for yourself. If you want to do some sweet stuffs, probably you need to harvest them later (you will mesh anyway). But if you want to sell figs, harvesting dates are more important so that not all producers will fill market in few days (which is not the optimal date for you, but for seller/market in general). Commercially, harvesting is usually done too early (so that figs [but also for most of vegetables and fruits] will not overripe or break during transportation). Again: for processing food figs may be harvest on better days (if you have some processing facility).
BTW I do not think birds will eat them. it is not an easy fruits for birds, so they tend to eat figs only when they are way over-ripen (so open). Mammals instead like them.