@Seramis Hi !
First of all, I summon @ian57 as he is the one who knows most abt screens. But it seems to me this one is connected on the SPI, soe you'll get a very poor performance on it as the FPS is really low on it.

concerning the switch between hdmi output or "any other video output", i'm not so sure ... Let's say that i've only found hacks to do that, but no easy process. I've found some interesting doc from raspberry for some "multi monitor definition", but i'm afraid it won't be enough