Receiving data from phones to Arduino via WIFI

Can Arduino Wi-Fi rev 2 receive real time sensory data from a mobile phone and act on it, if this is possible, what protocol should i work on it, i am a beginner

Can the Arduino Wi-Fi rev 2 run a webserver ?

Technically yes if both your smartphone and Arduino have IP reachability then an IP based conversation can take place.

how do you plan to export the data from the phone? Programming a mobile phone is not a beginner task... (even if MIT App Inventor can help, it won't solve every possible case)

More info is probably needed for guidance.