the black mat screwed on the ceiling of my hood probally serves the function of keeping the engine warmer, well ...
if i took it off would the engine stay cooler?
would anything bad happen?

I have seen other people doing it in pictures.
there is also a sqwege infront of the mat, should i leave that alone?

Its called a hood insulator and it protects the paint from engine heat.
Your hood paint might bubble if you remove it and experience high engine heat.

That insulator will not make your engine heat up. I saw the same engine temps with it on or off, both before and after my hood vents were installed.

It does nothing for your engine, Its there for your paint. Plus if something brakes like a belt & you dont have the insulator it might dent your hood.