I’m certain it’s for the grapple gun, that was my assumption from day one. People are bizarreInterestingly, these pics have generated some 'controversy' about Batman carrying a pistol. Personally, I suspect the drop holster is for his grapple-gun, but I could be wrong of course.
As do I. I'd like to extrapolate the design of what is under the armor based on what little can be seen. It looks fairly well fitted, but still allowing for more ease of movement than a typical one piece race suit.I tend to assume all of that was custom fabricated along with the armor, though you're probably right about the influences on it