i jumped the self hosting wagon 2~ years ago.
some inputs
1. go with a cheap vps and check the IP blacklisting
https://videos.lukesmith.xyz/w/f9pZjSNLHVZ4FFkdnxNaCU
https://videos.lukesmith.xyz/w/c1d4KKBe8iQ3sqL6W8vYDp
if you get a bad ip, ask your vps provider to get it changed. (and open smtp if not otherwise)
2. you will have problems sending to outlook/gmail for a few weeks. your emails will go directly to spam so you have to call your recipients and have them "mark as not spam". this happens separately with or without attachments so it will take some time...
3. i used mailinabox but there are other alternatives so this can be as easy or as customizable as you want.
4. you will be responsible for managing the domain and keep paying for the VPS (dont do anything stupid on the server because that might end your vps in trouble with the provider)
5. use backups for the server, backblaze b2 works nice and has 10GB free so yeah
6. i have used the server exclusively for work and i have found in my testing, i got emails a tad bit faster than gmail but i cant say with certainty.
about your questions.
1. if your "server" goes down, you can spin one up and "receive" the email in an emergency or you can (if you have backups), restore the same and work away...
you own the server so its not like your account will get deleted or anything. anything@anything.com will always be with you so as long as your third party has banned your domain, you should be able to receive the email.
> I wouldn't want that to happen if I needed to receive a confirmation email for, let's say, password recovery for a website.
this is a valid question. so your email goes down and you have to reset a password, no problem. as i already said, you just restore your backup and you will get the email.