Connecting NodeMCU through internet
How can I address the NodeMCU from the website?


You can't. The NodeMcu is behind the phone, behind a router, behind a gateway of the operator etc. It can access the Internet over the infrastructure routing it out, but is not visible from the Internet.


  Does the NodeMCU need to be a server or just a client?


The device should be a client and open the communication to the server by sending a request and renewing the connection if it times out. You can use WebSockets or MQTT or similar framework.