Basically, what the FAQ confirms is that items 1 & 2 from my previous post are possible.
Actually, 2 is not. You can't press "pause" or "rewind" on a live radio broadcast because the only way to record it is to listen to it. And as you've already surmised, 3 and 4 are not possible. Patrick's tuner can't change the signal routing in the player and doesn't change the player's capabilities.
Item 1, recording radio audio while the car is parked, is theoretically possible, but you would have to write the software to do it. That's why the FAQ says "If you are a software developer and you want to see about implementing this sort of thing yourself, you're welcome to give it a shot."
But the tone of your initial post didn't seem to say "I am a software developer and I am beginning work on this project, I would like some pointers." Now, if your goal was to try to prod a programmer into doing the project for you, that's fine, say so up front. Perhaps in the Programming forum...