You’re in Safe search: strict mode. It probably thinks it’s a term for porn and therefore blocks it completely. Set it to moderate or off and you’ll get results.

I don't see how this is an issue. I would assume self-hosting refers to some VPS at some hosting provider, so the IP doesn't matter anyways. Of course, if they are talking about hosting at home, then yes. But in this case they'll probably have a hard time opening receiving ports for email anyways, I could imagine. At least I would block these ports if I were an ISP for end users.

I think after a few hours the sending mail server will start notifying users of an undeliverable message but will still retry. But of course everyone can configure that themselves, so I don't know exactly what is typical in this case. I personally wouldn't want a downtime of more than 6 hours for my mailserver.

Yes, adding a second MX should work. Though I could imagine that this server will get some mails regardless, as there may sometimes be a temporary disruption for just a few seconds on your main mail server (network is funny), in which case the sending server will probably attempt to deliver to the second MX right away, instead of retrying the first one in a few minutes. So make sure you don't miss any emails because you forget to check the second email provider.

I don't see anything wrong with self-hosting the receiving part. Especially with something like mailcow it shouldn't be any more difficult than hosting anything else, provided you have backups in place and will be able to get the server up and running again within 24 hours to not lose any emails. Yes, spam may be an issue, but mailcow has useful defaults configured and it works okay-ish for me.

Btw, they also allow for configuring outbound relays quite easily. This allows for simpler configuration on the client-side. I have it set up so that all emails sent through mailcow will be forwarded to mailgun, for example.