“Add New” button on custom post type grid

As per comments you likely you want to use native editor rather than build one from scratch.

From poking through the core source outputting the link for that would be along the lines of:

$post_new_file = "post-new.php?post_type=$post_type"

if ( isset( $post_new_file ) && current_user_can( $post_type_object->cap->create_posts ) )
    echo ' <a href="' . esc_url( admin_url( $post_new_file ) ) . '" class="page-title-action">' . esc_html( $post_type_object->labels->add_new ) . '</a>';

Editor links for existing posts are easier with dedicated get_edit_post_link() function for them.

Having that you can customize editor experience via your CPT registration (you can declare if you want title, editor, and so on) and by adding additional metabox to it (there are a lot of solutions for that around).