I thought I'd take 10GB/20GB from the /home partition and transfer it to /var. It's possible ?
No, it is not. First of all, what you have are not partitions. Those are shares on the server which are defined by the server's admin. To change sizes of these volumes you must talk with your sysadmin.
I have seen this post but it seems to me the ideal solution
Yes you can make symbolic links from one mounted volume to another mounted volume, effectively moving folders. And if the application which uses these folders opens them by regular means - it would work.
Unfortunately, it is not always a case and sometimes the application requires a real folder, or at least a hard link (which does not work across volumes).
And anyway, you have to be very careful what are symlinking in the tree. It is very easy to ruin everything.
So I really discourage you to do this task yourself. Talk with system administrator who made the virtual machine for you.