Birch trunk question
The best approach is to actually let the tree heal on its own naturally. This appears to actually be an aspen tree, Populus tremuloides. It is tempting to cover the wound with something, but letting the tree heal on its own is the best practice. I would suggest making sure the tree gets plenty of water throughout the summer and add some fertilizer. You can use tree spikes or another type of fertilizer recommended for deciduous trees. It appears that the tree is also showing signs of chlorosis. You can add iron to the soil as an amendment or a liquid form of iron chelates that is sprayed on the leaves.
If you have other questions please let me know. Here is a resource for iron chlorosis, http://www.wyoextension.org/agpubs/pubs/B-1097R.pdf, and the Barnyards and Backyards website has lots of other information related to tree care http://www.uwyo.edu/barnbackyard/.