How to get my Back To Site button to point to the correct location?
You're just stating facts, that is how Drupal works. If you log in, you go to your profile site by default. That might not make sense for most sites, but that's what it does by default, there modules that allow you to change it.

And "Back to Site" takes you back you the last non-admin page you were on. If you are on the homepage, it will point you back to that. Again, that's a feature, not a bug