For starters, that "leaked" NX controller is a fake. It's really convincing, but the controller that we have on our devkit is nothing like that.
Our devkit's controller:
Doesn't have an oval screen. Ours is a standard rectangle.
Has physical buttons with a screen behind them. It doesn't have a form shifting screen, nor does it have a touchscreen with haptic feedback.
Is hardwired to the devkit, which looks like a boring black box with some USB ports and a disc drive.
However, that fake does get a couple things right. It does have scroll wheel shoulder buttons, but in addition to them it also has two regular shoulder buttons labeled ZL and ZR. It also has a headphone jack in the bottom of the controller.
Some other things I can tell you:
I don't know if the NX is backwards compatible with the Wii U or 3DS or not, but it doesn't look like it is. The system is different enough from both that I think it would be hard to play games from other consoles.
The controller is sort of a game system in its own, but it's not a replacement for the 3DS. It works like a companion app on a phone, and you can take it with you and control some things from your game, like how the VMU on the Dreamcast let you take a Chao with you and train it.
No one outside Nintendo knows what the NX's name is. It's still the NX here internally.