Ive been trying to do some googling to find out what this exactly is, but cant really find it...as I really dont know what to search...haha.

So, my question is, what is this piece that is broken? Can I fix it myself? And how critical is it? As in, should I not drive it again until I get it replaced?

Thanks

 

PCV breather hose. You can drive it. You can fix it yourself. There's a write up out there somewhere on replacement.