So in yesterdays game I had a situation where a rune golem in a forest, was smashing my Reanimates. In his godlike smash he separated reanimates away from Terrain. Does the Rune Golem get to close in and leave terrain in contact with the reanimates?

Well, close in would give you a speed one shift, as long as that shift left you engaged.

If you shift in terrain, you exit, and cannot touch any obstacles.

If you can't touch an obstacle, you can't engage. If you can't engage, you can't close in.

So no, you can't. You just stay in terrain.

You can usually choose targets that don't separate you from contact though.

In the specific situation a 2x2 Reanimates unit just shifted out of the terrain in question, in such a way that only it's back lane was touching the terrain with it's side... And then the Golem took the terrain and atacked them, destroying both back Trays in one swoop.

Speaking about... how do you place units when exiting terrain? Does any point of the side have to be touching it? or if you're wider, maybe every Tray possible must be touching it(that would make much more sense).

It's just any part of the edge - back edge for a March, side or front edge for a Shift (Rule 81.4).