Protocol for WiFi network to connect to a website?
1.) Whatever you'd like. There are wifi modules out there that can do both UART and SPI even. Example: http://www.rovingnetworks.com/products/Wi_Fi_Modules

2.) I'm not a web developer but I think in terms of minimum requirements you need to be able to open an http or tcp/udp connection with the server and do GETs and POSTs