Kingdom Hearts 2.5 HD ReMix will come out in Japan on October 2nd of this year, and will be released in North America on December 2nd. The game will also be released in Australia and Europe on December 4th and 5th respectively.
As for Kingdom Hearts III, I do have some bad news. Kingdom Hearts III, beyond the brief teaser featured in the trailer I've linked below, will not be making an appearance at E3 this year. To make matters worse, Final Fantasy XV will also not be present at E3. Square seems to be holding back for later conventions, likely Tokyo Game Show.
While the latter of this news is disappointing, I am happy to know that 2.5 HD Remix will be released in 2014 as Square Enix promised. Check out the trailer:
That's all for now folks, next week we will see if any of my other predictions are right or not. Stay tuned!