@jwnz
For the "manage external auth", you can set the Site Setting Authentication/Registration/ExternalLoginEnabled to false
This should hide that option
I can't find a way to hide the profile menu there from the left menu structure.
Basically, what that is doing is rendering any links from your Profile Web Link Set
You can hide it by adding JS in the Profile Web Page (that JS will load on the page, so any client-side customization you want, you can do there)
$(document).ready(function(){
$(".profile-info").next().hide();
});