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).