It's Forest what isn't so scary as Forbidden Forest in Hogwarts but still here live some creatures, who are dangerous. So you still need to be careful if you go in there. It's not forbidden to go there.
It's small lake on Ilvernormy grounds. It has crystal clear water, so you see end of the bottom of the lake. It's not very high for sure, only 4 meters.
The tree did grow to a place where one of the founders Isolde had buried down her old Salzar Slytherin wand what she used to have but due somethings lost ability to be used for magic. Over years tree grows and it couldn't be killed. Also, this tree leaves seems to contain powerful medicinal properties. So it's used now here in school only.