Well, make sure the “My Templates” or “Elementor Template” post type is not selected to return as a search result. Those are storage only post types used by Elementor to define page templates – they are not for displaying purposes.
You can check that on the General Options -> Sources panel: https://i.imgur.com/Z1iL9ik.png
Q2:
Yes, but you may need a small custom code snippet to replace with a space. This knowledge base should contain exactly what you need.