ED2:"Diamond" by alan *UPDATED!*
As expected, more details have come in. The name of the song is "Essence of me" "Diamond" and the initial version came out only a few days ago as part of her new album, "my life".
"Essence of me" and another song, "Over the clouds" will be re-released and re-arranged as part of a single this coming January. With that in mind, I cannot say with any degree of certainty as to whether the single version we hear this weekend will differ at all from the currently available version. All I know is that the single version of the song will be the version promoted for Inuyasha Final Act. For what it's worth, it's not unusual for a song to be re-recorded and resampled before or while being used in an opening or ending. "ALONES" (Bleach OP6, Aqua Timez) and "ANGELUS" (Inuyasha OP6, Hitomi Shimatani) are good examples of this as both were tweaked half-way through their runs.
At any rate, you can listen to the "my life" album version of the full song here. The song starts out a bit crappy, but it gets progressively more awesome and J-Pop. But like I said, I'm not sure of which version or parts of the song Sunrise and avex will use for the TV-friendly 90 second version.
Source: Channel-Ai
Edit: There's a temporary Inuyasha merchandise store opening in a Tokyo mall for a few days this December. Also, the full version of the opening, "A Future Without You" came out a few days ago. As for "With You" by AAA, the full version came out a while ago.