Here are my quick 2 cents on this:
NX is a new console that will initially be released as a "third tier" the way the DS was. If successful, the Wii U and/or the 3DS (if it is indeed the integrated console of legend) will be quietly and quickly retired within a year.
It will launch in November 2016, following the timetable of announcement-to-release of most recent Nintendo hardware, particularly the Wii U and 3DS, which had less than 18 months before announcement and release.
It will not carry the Wii moniker, which has been badly tarnished by the Wii U.
It will not have a GamePad-like controller, as the GamePad has largely failed to live up to it's promises, and has been quite frequently noted as a thorn in the side of the console actually preventing sales.
I would not be surprised if Zelda U became Zelda NX, or pulled a cross-platform release like Twilight Princess.
I also think it's extremely important to launch no later than 2016--and Iwata has made mention of "returning to Nintendo-like profits" by the end of the fiscal year ending March 2017, which likely indicates a 2016 release. Primarily because the Wii U is already moving into it's end-of-cycle decline like the N64, GameCube, and Wii during their final two years on the market and the total lack of 3rd party support supports the hypothesis of "end of cycle" decline.
The big problem, however, is that the Steam Machines are launching this year, which means Nintendo will be launching in the face of three strong competitors, two of whom (PS4 and XBO) will be planted firmly in their peak years (2016~2018), which means it will be extremely difficult for Nintendo to even be noticed in this crowd, particularly when they are barely registering to consumers now as it is.
Guaranteed the NX will not be out in 2016. It has no reason to rush out. Sure, the Wii U isn't gonna be the big seller it was hoped to be, but it's turned around and it's doing alright for now and it'll keep that going till I feel a 2017 release. That gives the Wii U a comfortable 5 years of prominence.
I do agree it'll drop the Wii name, it has to (And don't you even dare of adding NEW onto it, Nintendo. That's the worst thing you could possibly more than keeping the Wii name lol).
And the Zelda is guaranteed for Wii U. The Wii U has not had it's Zelda game and they aren't going to pass it over simply because it would be a disservice to those who supported the Wii U. I don't even think the Twilight Princess deal will happen, but perhaps an enhanced edition showing up within the first year or so on the NX, like Wind Waker HD.
I actually think the gamepad is pretty great, kinda the only good addition the current gen systems have had, even if it hasn't had full support, I liked being able to have a separate screen and such, but it would be smarter to go for a more traditional controller route, using that extra money to beef up the games hardware to make it more competitive, but still affordable in comparison to the other systems.