Re: Slash chords
Typically, when ppl talk about Slash Chords, they talk of triads with a particular note in the bass that is NOT IS THE CHORD.
Your examples look more like inversions.
c/e is a 1st inv. c chord.
f/a is a 1st inv. f chord.
f/Bb is a 2nd inv. Bb chord
D/E is a slash chord played by voicing a D maj. triad and throwing an E in the bass.