Hey Ryan, so when PG talks about the A minor chord being in the C Major chord family, it just means that in order to do the C major scale with chords, you will have to play the A minor. Now, as for the theory of why, the long story short is that A minor is made up of all the notes that are in the C major scale (AKA: Natural notes (no # or b)) while the A Major chords has sharps (#). Reason that it's minor being that A is the relative minor of C (you will see that later). So while yes it's a minor, the way it sounds is necessary to stay in the key of C.
Let me know if this is a clear explanation, I tried to keep it short.
Now, the pentatonic scale is something that can be played over the chords you mentioned. But it all depends on which pentatonic scale you do because the pentatonic scale is a pattern of notes that all depend on the root that is given. The pentatonic chord learned at the beginning of the lesson is C so therefore, yes.