Hi all! :)
*editing to add* I forgot to say that I'm located in South Australia, if that helps with the identification. It is summer here now, and the fruit has been there for a little while, but none have dropped onto the ground.
I have a question about what kind of fig tree is in my back yard, and also a small concern over the sap.
Some of the leaves measure 30cms from stem to tip, the tree itself is massive, 12-15 metres maybe? (I'm not good at judging heights, but it is twice the height of the house). The fruit is all green, and small to medium size. I don't know much about what is "big" for a fig though, it's say the length of a matchbox as a large one.

Leaf (big one)

Leaf (medium) with the fruit around it.

The inside of the fruit


The fruit

You can see that there is a big blob of white sap on the upper one, this is what was on the edges of all the fruit too.
Now, here comes my moment of incredible genius... :(
I see it through the window when I am at my computer desk, and noticed some birds feeding on a fruit that was slit open. I thought I would cut the tops off some of the fruit to encourage the birds to come back.
I got my hands covered in white sticky glue-like sap that took a while to get off (parts of my hand that was holding the tops of the fruit I cut open is still tacky). I googled the sap and read that there can be some pretty dramatic effects, especially if it's mixed with sunlight. I am sure the cases I saw were extreme, so I was wondering what (if any) reaction is normal? I didn't feel any sap from the branch, and didn't cut or touch the leaves, just took the tops of the fruit.
Many thanks for reading this :) I have a new interest in figs.