When Boys & Girls PV was released?
 

Since the single Boys & Girls released before LOVEppears doesn't include the "original mix" track I wonder, was Boys & Girls PV used to promote the single or the album (LOVEppears)?

:)

The video came out before the single. The CM to promote the single uses footage from the PV and also footage from another CM to promote KOSE.

^Then the song used in the PV is Boys & Girls - AUBE Original mix?

Yes. The original version of Boys & Girls just happens to also have the "AUBE" brand name included in its title. The LOVEppears album uses the same mix (one of the few examples of that happening on that particular album lol).