Save Post. Check Links.

No, but it will automatically find any broken URLs in a post and list them for you, so you can review and correct them.

Yes, the plugin will ping every URL in your post’s content, no matter if it’s in a link, an image** or even in a shortcode.

No, it will just list any broken URLs for you, but it will do so already when you save a draft. Most people save a draft multiple times before they publish it, so there’s a fair chance you’ll notice any broken links before actually publishing.

By default the plugin will try to ping both, http and https URLs. If needed, you can change accepted protocols via hook. For example, in order to check only URLs with SSL:

add_filter( 'spcl_acceptable_protocols', 'set_spcl_acceptable_protocols' );
function set_spcl_acceptable_protocols( $schemes ) {
    return array( 'https' );
}

There is none, no configuration necessary.