Have you searched the Forum? There is also something in the Cookbook and an FAQ here on the Forum.
You need a reverse proxy to do what you are asking for.
No it isn't. Node-RED is a "microservice". It includes a limited web server that exposes a single port. You might have many instances of Node-RED plus other node.js, Python, Rust, Go, ... web servers all running either on the same device or across your internal network.
Proxying them to the outside world is a specialist task that requires a specialist service.
There are also security considerations to be taken into account when you expose a web service to the 7 billion human beings and untold automated bots in the world. Again, this is best dealt with using specialist tools.
So no, not crazy at all.
