I know and I kinda hate its name for it...

I could have sworn it also had an option to only allow HTTPS connections with error as fallback. But I guess I saw that in some other add-on. Sorry for the false information!

Yes to both, but I meant a search engine that only gives results which, themselves, use https. Either a standalone search engine or as a DDG or Google query flag, e.g.,

query: home siding repair -protocol:http