The tube is routed correctly. From the valve cover to the air cleaner.
Other models have other routes, for instance one of my cars goes from
valve cover to intake manifold, but same purpose.
Yours is better.
Three ten mm nuts hold the air cleaner housing onto the intake manifold.
Remove them (if these are the melted things you mentioned, replace those
rubber mounts with dealer supplied parts). Underneath the air cleaner
housing you might have a tube that goes down to the oil pan.
It is supposed to have a one way valve allowing oil to flow into the pan.
Other threads describe that this valve can go bad.
I do not have any experience with this.
This replacement tube is also designed to help minimize oil in filter:
http://www.**************.com/store/item.php?item=Turbo%20Diesel%20Breather%20Upgrade
Take it apart, get it cleaned out.
And like the others said, get that air filter in there.