Oh god, yeah. I personally would not try to self host e-mail or any service that you need other people to be able to reliably connect to without a static IP. As to losing power… In theory mail servers are supposed to queue mail and resend later, and you can also set up a backup MX that will queue mail for you (senders will automatically switch to the backup mail server if they cannot connect to your primary one). There are even free services for backup MX junkemailfilter.com/…/free_mx_backup_service.html (though they use this to train spam filters, so if you have privacy concerns you may want to avoid it). In the past I have had some prolonged downtime on my mail server and I have noticed that some senders will give up entirely and never send to that address anymore (which I think is poor form on their part, especially since somebody could register that email account later). I’ve since setup my own backup MX to avoid these issues, and it’s worked great when my primary has had network issues (needed a spare box for backup nameserver and stuff anyway, haha).
You absolutely can use an external mail service as a catchall with your own domain. For instance protonmail has support for this:
You’d have to look into the pricing and read the fine print, though. A lot of mail providers charge per inbox and I’m not sure if they’d charge extra for catchall services or not.