I don't mean to offend, but I think you need much more practice, using the chords to accompany melodies, for the theory to make sense. Do you know what it means that a song is "in a key"? How many songs have you played, with melody and chords, in Ab major? How many in F minor? Have you used the chords you listed in the songs? Have you tried substituting the chords with different chords? Have you ever played a song where the melody has the note Db, and for it the suggested accompaniment chord is Bbm6/G? Have you tried playing a Bb/G or Gm7 as accompaniment for that Db note? How did it work - did it feel better or worse in that context?
If you have never played a song where a Bbm6/G chord is used to accompany a Db note, then where have you seen it used? What melody notes were there? For songs that are in the key of A minor, you're looking for a melody note F and accompaniment chord Dm6/B. If you've never encountered such a song, then you need much, much more actual practice, less theory. :)