most display elements are theme driving with template functions just like in wp…
so if you want to remove an element, just remove the template function that displays it… or you can change the situation under which the element is displayed…
fyi, login changes to logout after logging in… and registration is not available while logged in either..
most of the buttons you are referencing are in the spHead.php template file of your sp theme…
as always, we strongly urge you to make a child sp theme or your own sp theme before making any changes so you dont lose them on updates… for more info on these, see our codex links in sidebar…
as to the breadcrumbs question, see this codex article on the template function for displaying them:
https://simple-press.com/documentation/codex/api/template-functions-and-the-api/display-template-functions/common-view/sp_breadcrumbs/
it shows you how to remove elements via arguments to the template functions… if you dont want any breadcrumbs, just remove the template function from your theme…