[u801e]

> git rev-parse branch-name: gets the hash of a branch name, useful for verifying two branches are at the same place

I believe the same thing can be done by running git log --oneline -n1 branch-name (though you will also get the commit message title in addition to the sha).

> my_branch^ points to the commit 1 before my_branch, and can be repeated multiple times, ie. my_branch^^^ to get the commit 3 from the top.

The ^ notation only references the first parent of the commit. You would have to do something like commitish^2 to reference the second parent (though this would only be an issue for merge commits or any commit that has more than one parent).