Hi,
IMO, for the sap, this is insect damage. Did you pinch the stem or did an insect mess it up too ?
If so then you've got two hints saying that you have an "horrible" insect to get rid of ( insects are all horrible when they attack my trees).
But, it is common to lose some figs before they get a chance to ripen .
I had some turn dark and fall already. Could be sun burn or the tree not feeding that fig properly (possibly lack of water or root-bound ) ... Nothing one can help immediately.
Keep hoping for the remaining one to ripen.
Did that tree already fruit for you ? ( as in: are you sure that it is not an unknown strain of the smyrna type ?)
Well wait and see.
Keep the tree well cared (water and fertilizer) so that you have no regrets if the fruits all go wrong.