Hi, I recently set up my own email server

• It's a huge pain in the ass getting things like DMARC and DKIM and whatever to work. Without those, most providers won't even deliver your messages. But luckily, there are websites that help you check and fix your configuration
• Even once you do get these things set up correctly, most providers will send your outgoing messages straight to the recipient's spam folder
• That being said, I believe most providers will mark you as "not spam" if the other person initiates the conversation. So this could be a non-problem if you're making an email for your business and putting it on business cards or something.
• Mullvad (VPN provider) self-hosts their support email, and they seem to be doing fine.

Hope that helps

Yes. I host my own using Mailu.io. With the proper records, you will be able to send emails to any big email provider (proton, gmail, outlook). You need to pick a good TLD (.com, .net, .org, etc) so you don't get your email thrown into the spam folder immediately.

If you buy a domain now, you will probably get on the Spamhaus blacklist, which every big email service seems to use (again, proton, gmail, outlook, and probably others), so you will need to wait a few months and keep a good spam record (well, don't send spam emails obviously and keep your email server with the proper configurations).

Also, pick a good VPS provider (No vultr, no linode) with low levels of abuse, because if you setup your email server in an IP range with a lot of abusers, you may get your email flagged. (You can check that using https://www.uceprotect.net/en/rblcheck.php, but I'm not sure if uceprotect is trustable).

You can host your domain pretty much anywhere and they will provide mail hosting as part of most packages. From there, it's up to you to talk to their servers to manage your mails, typically through IMAP.

Hosting companies will be whitelisted as far as mail routing is concerned.