p.4 #1 · Which manufacturer has the most intuitive UI?
Sony NEX is the only UI I've ever considered to be bad. I'm with whomever said they wanted to throw their camera against the wall.
When I consider what the OP is working on I imagine a totally configurable camera, mostly using touchscreen, very similar to a Logitech Harmony universal remote control. So beyond some very common buttons and dials you'd be able to create touch "buttons" and configure them to your screen in whatever way makes sense for you. We'd all theoretically have our own version of the same camera.
Having said that, I'm all for more manual, direct controls. But I think I can see in to the future on this one.
p.4 #2 · Which manufacturer has the most intuitive UI?
That's a hard survey to answer as there are some significant differences between camera models (e.g. Sony NEX vs. A-99) and some cameras have great menus but clunky physical interfaces. Here are some of my observations on cameras I've actually owned:
Panasonic G-1, GH-2... great menus ... average physical interface
Olympus E5-M ... terrible UI all the way around (good thing is has great IQ)
Sony A99 ... average menus ... good physical interface
Sony A7II ... average menus ... great physical interface
p.4 #3 · Which manufacturer has the most intuitive UI?
I presently have Leica M, Canon (FF and APS-c), Olympus and Panasonic cameras. I've used or owned a lot of others, including Nikon, Sony, Epson, and Ricoh.
Leica is definitely the best as you have everything you need and no more, laid out in a relatively intuitive way. Canon and Nikon aren't bad, but hardly as good. Ricoh is quite good, and better than Canon/Nikon. Sony is the worst, followed closely by Olympus. Panasonic is midfield.
Leica M is of course a simpler camera, but that and it's excellent UI are both its strong and in many cases weak points. If you know what you're doing and are used to manual focus rangefinders, the Leicas can most easily 'disappear' between you and your subjects in a way that takes way, way longer for a Canon or Nikon to do, if ever.