I found some but not a lot of the fruits that are having black spots as per image attached. Why this happened ? Should I remove those ?

Possibly sun burnt. Happened to my Ariane fig last season.

Hi,
IMO, not a disease, let them on the tree.
For me it is rubbing damage. Could be people passing by and rubbing with shoulders or could be a nearby object or branch rubbing when wind blows.

I have same problem, but not as bad as your, My tree is located as windy corner, I don't know why this year, when fig @ younger stage, Even Fig leaves rubbed on figs and it caused black marks after 1 month.
   

Sometimes fruits get spots like this on them for any number of reasons.  The fruit will still ripen and be edible, but there will be a little tough spot on the skin.  I wouldn't worry about it.

Definitely rubbing damage caused by its own leaves, just callused skin... No biggie, still edible just doesn't look appealing...

I agree with Simon also... superficial rubbing damage from the wind blowing the leaves.

Great thanks to all for your valuable comments.