I think it'll get announced at E3 2016, release in Japan Holiday 2016, and then release everywhere else Spring 2017. I don't know what they'll have for launch. Probably the next 3D Mario game? Other than that, all I know is that if they want to have games lined up for launch and after, then they're going to have to have teams start working on games for the system now. Which means the 3DS lineup for 2015 and especially next year isn't likely to have a lot of games. I wouldn't be surprised if they port more Wii games to N3DS to fill some gaps.

I would also be okay with holiday 2017, if they have to release the new one quickly.

I think 2016 is really soon for the next handheld. I guess it will come out 2017, with the home console counterpart. About the launch titles, I think the best ones would be the 7th Gen of Pokémon (because that sells a lot), a Mario game (at this point all of them are just fillers, but everybody like them anyway) and a Metroid game.

This way they can reach to the main niche gamers (the RPG lovers, the casual ones and the "hardcore" gamers). Of course, 3rd party and maybe a remake would be present too.

Everyone is so optimistic about a Luigi's Mansion 3, hope they make it, 1 and 2 were both amazing games to me.

Launches have historically only gotten worse, across all platforms. The HDS will launch with some mini game collection, a soccer game, another Pilotwings, and yet another port of Rayman 3D.

If the 3DS couldn't even launch with a port of an N64 game, I have no hope that there will be anything to play on the next Nintendo handheld for probably one or two years after launch. (Hell, even the DS took about a million years to actually release something worth buying the system for.)

I think a Mario Galaxy HD/3D pack might be a plausible candidate. Perhaps the next 3D Mario instead, that might happen.
Along with Mario Kart 9, which seems very doable, re-using the engine and assets from MK8.
Then some casual title along the lines of Brain Training, and maybe some lesser 1st party IP like Wave Race or something.

A 3D Mario will launch with the next handheld in addition to the new home console. Yep.

I could see something like that, though I think they could have Mario Kart 9 for holiday 2016 too, the gap between MK7 and MK8 was 2 1/2 years, 2 1/2 years from May 2014 is pretty much December 2016, so it could make it I guess. 

But yeah I can agree with that too. 

May 2016 - Nintendo Fusion Handheld Launch (Japan w/US and Europe following in June/July):

Animal Crossing (big title), F-Zero (smaller title), third party stuff. 

June-October 2016 (post-launch period)

Luigi's Mansion 3, SMT x Fire Emblem (Wii U dual release)

November 2016 - Nintendo Fusion Home Version Launch

Super Mario Galaxy 3 (worldwide), Monster Hunter 5 (Japan)

The post launch period still kinda worries me though, Luigi's Mansion 3 is a pretty big title, but maybe not big enough to prevent a post launch lull and that's really hurt Nintendo in both of the last 2 cycle launches. Maybe add Hyrule Warriors 2 into that window? Mario Maker 2.0? 

I think Dragon Quest, like the Final Fantasy series has will go multiplat for 2017. Playstation 3/4 + Nintendo Fusion (Home and Portable) for DQXI. 

F-Zero, Pikmin 4, a 3D Mario, and a Zelda remake would be good for me

Tecmo-Koei works pretty fast, I think they could pump out a Hyrule Warriors 2 in a fairly straight forward manner.

I think some ports of Wii U games that enough people didn't play the first time around could be feasible too ... Donkey Kong Country: Tropical Freeze deserved to be enjoyed by more people. Add an "easy mode" and a few extra levels with faster loading times and I'd double dip to play it again on the go. Pikmin 3 could fall into this category too.