The general recommendation for fixing supports cheaply is to fit a single, large lag bolt into a cleanly drilled pilot hole. This reduces the number of puncture points to one, and eliminates dangerous problems of compartmentalisation
Nails and screws are not strong enough for treehouse loads, especially when storms twist the structure.
Support beams should not be bolted directly to more than one point, because the tree will not be able to move freely in the wind. This will build up very large forces in the support and risks failure of the attachment points. Instead use a flexible support bracket at one end of the beam, or use steel cables to suspend one end.