Your issue #1 is normal behaviour of the camera if you shoot long exposures with the "long exposure mode" on as the camera locks up during its dark-frame exposure before writing to the card. With a 10s exposure, the dark frame exposure will be 10s too, and if you don't know this, it seems like the camera has locked up.
Black frames: No comments.
Wobbly shutter button: Mine is too, at least much more wobbly than the shutter on the X-Pro1. A bit annoying. And while we're at it. The dioptric adjustment button is wobbly/loose too and the adjustment is often knocked off when I just grab the camera. This button is a design error - What I really is replaceable dioptric lenses as on the X-Pro1!
Slower AF: I run my camera in "Normal mode", not "Hi perf" and I would say that it is on par with as I remember my X-T1 in most situations. I often use my X-Pro1 in combination with the X-Pro2 to avoid switching lenses in dusty conditions (doing some urbex photography) and yes, the X-Pro1 is sluggish in comparison to the X-Pro2.
Heating issue: Happened once while the camera was just a few hours old in my hands. The camera felt warm, so I turned it off and. It had lost all settings when I turned it on again. Fuji said that this is related to that the internal back-up battery has not reached nominal charge yet and advised to leave the camera off with a fully charged battery inserted for some hours to allow the back-up battery to charge. Since then the camera has worked flawlessly,
EVF color cast: I never noticed the blue cast until reading your post, but then I have assigned the "preview effect on/off" to the movie record button and is usually using the camera with this setting off. Also, if I don't remember wrong, the color balance of both the EVF and the LCD can be adjusted via the menus. I don't have the camera in front of me so I cannot verify this just now.
;-D Hans