Short answers, pulled from the story.
Capcom Classics Collection Volume 1 contains all sixteen games from the Capcom Generations and Street Fighter Collection 2 compilations, converted from those ports rather than the arcade originals, plus six additional emulated titles. It also features a Deluxe Versus Mode for the Street Fighter II games.
Capcom Classics Collection was developed by three studios: Backbone Entertainment, Sensory Sweep, and Klein Computer Entertainment. Klein Computer Entertainment also co-developed Volume 1 and handled the PSP version Reloaded, while Sensory Sweep developed the Game Boy Advance compilation Capcom Classics Mini-Mix.
Capcom Classics Collection Vol. 2 was released on the 14th of November 2006 in North America for PlayStation 2 and Xbox. It was not released in Japan.
Reloaded contains the sixteen games from Capcom Generations and Street Fighter Collection 2 plus Knights of the Round, Eco Fighters, and The King of Dragons, while Remixed covers most of the remaining games from the home console volumes. Remixed launched on the 22nd of March 2006 and Reloaded on the 24th of October 2006; only Reloaded was released in Japan.
Yes. Both Capcom Classics Collection Remixed and Reloaded for PSP can be played on the PlayStation Vita by downloading them on a PlayStation 3 and copying the files to the Vita via USB transfer.
Capcom Classics Mini-Mix includes three NES games: Bionic Commando (1988), Strider (1989), and Mighty Final Fight (1993). It was developed by Sensory Sweep and released on the 19th of September 2006, exclusively in North America.