Wi-Fi Module communication?
Good detective work so far!
In the admin page you found one can see the name of the module: HLK-RM04. Googling on that I found the manufacturer/seller page. 

A PDF with some information can be found here.

Also one link with somebody's experience with the module.

For other projects you might want to try as well the ESP8266 - very cheap and seems a lot of people have experience with it, so you might find more information on the net.