Since I've been baligh, I've prayed and fasted on and off and I have no idea how many prayers/fasts I've missed.
I'm pretty sure some years I haven't missed anything, and other years I've missed the majority. How do I determine how many prayers/fasts I have to make up? Also, some of the fasts missed were intentionally broken while some weren't, so how do i determine how many i have to do kaffarah for?

You have to first estimate to the best of your ability. It’s between you and Allah. Those that you know for sure u broke intentionally you must pay kaffara for.

After this, I recommend you do prayers and fast ‘ihtiyat’ just in case, to cover what was possibly missed.