What type of photography do you do? The biggest differences between the d600 and d810 are the greater dynamic range and the improved AF system on the d810.
Shoot RAW. Expose just slightly to the right to over expose the image a little. In post, correct your exposure, wb, etc. and then pull your shadows and blacks to get the details out of his fur.
These both refer to the physical size of the camera sensor. Dx is smaller than equivalent 35mm film size. Fx is equivalent in size to 35mm film. Your d7000 has a DX sensor.
The 6D isn't close. A good camera on it's own merits but outclassed by the D810 in just about every respect, unless you regulary shoot at 12800 or higher ISO.
I had a 650D before I switched to my D7100. Image quality between the two is comparable but I think there is more detail in the Nikon because of it's 24mp sensor. I switched because I got a chance to use a friend's D600 and liked the control setup of the Nikons better.
I had this problem with my d7100 when I ordered it. Straight outta the box it was doing this. Sent it back for an exchange. I'm guessing there is a problem with her sensor.
The 85 1.8G is a very sharp lens and on a dx body an excellant portrait length and focuses closely enpugh it's very nearly a macro. If you have a dx body, I'd say the 85mm. If you have a fx body the 105mm migt be better for you (I haven't used the 105 but I own the 85).
Go into your menu. You can try to figure what control setting you changed by going into the Custom Setting menu > f Controls, but if that doesn't help I'd reset everything. Go to Setup Menu > Reset user setting. Then go back and customize your controls.
SD cards do not slot to USB ports. Doesn't your Mac have a built in SD card slot? If not, then yes, you will need a USB3 compatible card reader to get the highest speed transfer.