I want to design a new cabinet and would appreciate your expert advice on the following points:
What should be the minimum gap between the doors to ensure smooth operation?
Kudos for the well-asked Question, but unfortunately the answer is: it depends.
Really the one and only place you'll get a definitive answer in advance is from a manufacturer; although of course for a known hinge you can get input from existing users in a suitable venue, the gapping someone else uses might not be down to spec but is instead based on another factor or factors (including their personal aesthetics, and simple ease-of-installation).
In the absence of the above then you'll need to find out empirically — that is, make some sort of simple mockup from scraps and find out how much clearance is actually needed, then proceed accordingly.
The issue is that "full-overlay concealed hinges" are not a single entity, that's merely a description of what they are and the function they provide. There are of course many similar hinges, but subtle differences between them could make enough difference that a stock answer – especially for minimum gap – wouldn't work for both cases; it only takes around 0.2mm / 0.008" to cause some binding.
