Some remixes can be downloaded from here:

??????????�??????? ????DL??????????? ? CAP'STONE???????????? ??WEB (http://www.capcom.co.jp/sound/discography/stxcap-00001/)

Niceee :D

How do you download from this site?

I would like to know that too. My Japanese isn't good enough to discern the instructions. :(

Anything that can grab media from a website will do. Like the DownloadHelper add-on for Firefox or the JDownloader. :)

I have upload all tracks in my YouTube channel : https://www.youtube.com/playlist?list=PLO_zMwj3nmg2DfA-CcBQU-5WmvKbxutzc

Thanks. :)

Is this the complete soundtrack?

Yes.

Is there an actual RIP of this discography somewhere? I would love to have this in FLAC

You can download all tracks here : http://forums.ffshrine.org/f72/~-mobile-games-soundtrack-~-179614/#post2768456