Recently my provider decided to randomly cancel my domain, getting it back from transfer with everything out of date was painful.
Basically, if you register your domain through namecheap, then after setting up email at *@ximeng.net, don't update your email address to be [email protected] when changing the rest of your accounts. Reason being, if for some reason there is a problem with the domain, you don't want your only means of fixing that problem to potentially be invalid.
Therefore it wouldn't be a bad idea to keep the account associated with your registrar still on the original Gmail address (or if you are really paranoid, create a new email address through someone like protonmail just for your registrar account).
I have to manage a domain and have a basic understanding of how DNS works, that is unavoidable.
DNS is a bit complicated to describe in short reply but on a very high level: say I register a domain example.com. Registrars usually give you an interface to manage DNS where you can set A records (association with IP), you basically put there 2-5 IP addresses of the DNS servers serving your domain. You can also setup MX records that are used to resolve mail servers for your domain. Setting up fastmail is simple: you tell them that you want them to serve mail for example.com and setup couple of MX records pointing to the Fastmail servers (they give you the full host names).
0) Get your own domain and set up MX record to fastmail servers
This way if you ever migrate again, you will not need to do it all over again. One word of advice - keep your registrar login and emails associated with the domains _not_ on your domain, otherwise it is going to present a problem should you ever need to fix anything related to domains.