Tree id

I just closed on a property in zone 8. Southeast Virginia.  There's some old large fig trees and Asian pear,  but I'm struggling to I'd some of the other trees because I've always lived in zone 6. Here's a picture of one.

Looks a lot like chinaberry (Melia azedarach) to me. How big are the fruits?

I believe you are correct.  The fruits are about 1" diameter.  Should I cut them down? It doesn't seem like they're useful for anything. Also,  here's one of the fig trees I found on the property

I'd get rid of it. Nothing edible, not good forage for livestock (toxic), and most pollinators dislike the flowers. The wood is high quality and can be used for cabinetwork. They're considered invasive in the South. Be warned that after you cut it down it may send up dozens or hundreds of suckers from the roots, like ailanthus.

Nice looking fig, though. Any fruit on it?

Tons of fruit...probably3-400 figs. However, there's a canopy of mimosa and a few other small deciduous trees over it that I think I should thin to let some direct sun on it to ensure ripening... your thoughts? PS- thank you for your responses so far... tremendously helpful

Yes, give it more sun and you'll get better/sweeter figs.

Or at least the birds will :-)