Adding/Changing Functionality of Custom Post Type Main Admin Page

Don’t have the direct answer myself, partially because I don’t know what you want to filter for. But did you check how some of the plugins do it? Here are two examples: Filter page by template, Parent page filter.

As for your second question, not sure if that’s possible. That also depends on how you have connected the form to the custom post type. You might have more luck creating separate questions and add more details.