My online community SDF was founded in 1987, four years before Tim Berners Lee invented the web. They are so old that their FAQ still refers to email as “Arpanet email”. Guess what? Emails from SDF don’t reach Big Tech servers. I’m positive that the beards of their admins are grayer than mine and they will have tried to tweak every nook and cranny available.
No, it will not. If it works at first, it won’t for long.
You can totally go to Hetzner, GoDaddy or other hosting providers, get a domain and send mails to Gmail.
No, you can’t. Read the blog for why you can’t.