The first rule of email is reliability, your home server tends to have a higher downtime than Gmail and it's more hassle than it's worth
If you want to get fancy get a domain and a 3th party to host it, self hosting is really unadvisable.
Any downtime us covered by backup mx somewhere
It's the common (mis)conception that self hosting email is impossible. That's not true though. Better be careful with your IP reputation but aside from that, it's definitely possible. I've been self hosting e-mail since 2000.
Same. I've been self hosting since the early 90's, starting with a UUCP feed. Over the years, I've used smail, sendmail, qmail, postfix...