Also, is there anything stating that you can only take free actions on your turn? I genuinely don't know... seems weird, if talking is actually considered a free action, since then you could only talk IC on your turn in combat. If you can take free actions when it isn't your turn, then you can fall prone when it isn't your turn.
Edit: I checked - the definition of 'free action' doesn't specify that you can't take them on others' turns, but earlier on when describing actions in general it says you take actions during your turn, and it specifically points out intermediate actions as an exception. Likewise, it lists talking as a free action and specifically says you can talk when it isn't your turn. So no help there.
And yeah, being forced to fall prone doesn't require an action of any kind. If you cast hideous laughter or gust of wind on a creature (size Small, for gust of wind), they immediately fall prone, yes? You don't wait for their turn for them to fall down; that makes no sense - they're being forced to fall down, not choosing to do so. Same for successful trip attempts. Same for people who fall unconscious.
With the AoO's... yeah, your DM is an ass. If you can't convince him that it does indeed require an action to provoke an AoO (with a few particular exceptions; I'm thinking of the feat that lets you make an AoO if you're opponent *doesn't* do something, but AFAIK that's one-of-a-kind), then you can at least remind him that you can only make 1 AoO per round, unless you have Combat Reflexes, and then you're limited to your Dex bonus+1 per round. Not much, but it may help a bit if all else fails.
Really though, I would question the motivation behind a DM who did something this blatantly stupid.