The Classical style pieces that Django recorded are as follows:
First movement of Bach's double violin concerto in D minor (2 versions)
Liebestraum Number 3 (Liszt)
Fantaisie Sur Une Danse Norvegienne De Grieg
Improvisation Sur La Symphonie No. 6 De Tchaikovsky
Django's Dream (Improvisation on Debussy's "Reverie", with the introduction taken from "Prelude a l'apres-midi d'un faune")
There might be one or two others that I missed.
Django also composed several "classical" works including his "Bolero", which was played at a concert that included Ravels famous piece, and also his Gypsy Mass of which only a fragment still survives played on organ. The score has unfortunately been lost.
Django composed by dictating the lines from his guitar to someone who could write the music down.
Django met Segovia on at least one occasion. There are, however, conflicting reports about Segovia's reaction. One story tells that Segovia listened entranced to Django playing solo, and when he had finished asked him where he might buy the music for the piece. Django laughed and said that he had just been improvising. The other story is that Segovia remained utterly unimpressed and blanked Django all night.