Hi @gumbelj,
We don't use self-registration, so I'm can't provide much help with issue #1.
For issue #2 though, if you need folks o access both login methods somewhat regularly, you'l probably want to set up a "discovery page" in your authentication settings. You can make a webpage with links to both login methods, then put that webpage URL as your discovery page. Any time a user needs to login, they'll be directed to the discovery page and click the proper login. Since it's just a webpage you can design and name things whatever you's like. Maybe a "student/teacher" login and a "parent login" or "external user" login, whatever makes the most sense for you. Here's a screenshot of ours:

Hope this helps!
-Chris