How to tie treehouse cross beam to tree branch notch without harming tree
You certainly won't want to just sit the beam in the fork of the tree. The tree will move quite a bit and you'd slowly wear through the bark and damage the tree if you do that. Also note that forks aren't always the strongest part of the tree. 

What you want to do is have the beam mounted to the tree with hardware that a) allows for lateral movement and b) is offset from the surface of the mark.

They make special hardware just for this. It's typically a huge lag bolt with a spacer than the beam 'rides' in via a slip bracket. Example:



source: http://www.treehousesupplies.com/1_25_Floating_Bracket_p/br-f1.25.htm