How do you interpret this couple of notations?
In Bar 2, Fm / Ab, what does the slash do? Do I play either chord or both?
In addition, in Bar 3, what does the /9 mean?
Fm/Ab stands for F minor with note Ab on bass. Generically, X/Y is Chord X with note Y as lowest note.
This second chord could be read as Gb major with major seventh and added 9th. The slash after a chord alteration serves only as a separator to indicate every simultaneous alteration you should apply to the chord.
Haoest, if you play melody in right hand and harmony in left, and if you play with bass player, you can simply play this progression:
Bbm chord: F-Ab-Bb-Db
Fm/Ab chord: F-Ab-C-Eb
Gbmaj chord: F-Gb-Bb-Db
Gbmaj9 chord: F-Gb-Ab-Bb-(Db)
The last chord will fit right, don't worry. The Db is optional since it the fifth. It will be more effective if you write what chords going next to determine more usefull order for the voices. But it's for next time i suppose.
These chords are known as slash chords or hybrid chords.
For example: C/B, where C is the chord and B is the bass note.
With a diagonal line, the symbol above refers to a chords while the one below to a bass note only.
Note that when there is a horizontal line, it refers to a different thing (polychord).
A slash chord might sound different from what it is. For instance (from Jazzology again):