If i'm playing Harmonic Minor in the key of C, does that mean i can play any chord over that as long as it's a C? What is it that determines what chords can be played over what scales in a certain key?

Simple explanation:

Not quite. The C Aeolian mode (I simplified Harmonic minor to natural minor here) contains the same notes as the E flat major scale, meaning that if you played a C minor chord, you'd be playing in the key of Eb. This would work. However, if you played a C major chord, you'd be playing notes from the C major scale, which corresponds to A minor, and this wouldn't work out. Start out by using this (and one of many modal explanations on this forum by now) to play in key, that'll be a good place to start.

By the way, both of the theory threads I've seen today mentioned harmonic minor. Where's the Spanish Phrygian love?

Spanish gypsy / Phrygian Dominant mate? :)

P.s What about Mohammedan? ;)

Yeah, I'm too used to hearing Spanish Phrygian that it's ingrained in my mind.

PS: What about the Greek mode names mishap? :)

Ha! Ha! I use the the different variations of the names/modes depending on who I'm talking to I suppose. A death metal/rock player will get Harm minor, Flamenco player will get Spanish gypsy and if I'm trying to appear all musical (when I don't know jackshit anyway) I come out with the Phrygian Dominant spiel! :lol:

The natural 1-3-5 chords that appear in that scale in particular are: C minor, D diminished, Eb augmented, F minor, G major, Ab major,and B Diminished. You can also use functional harmony and play G Phrygian Dominant/Spanish Gypsy (the only difference is the root note, its still the same key and notes). You can also build all your other chords off these chords I listed here.