Is it okay to ask the Call Sign of the plane to Pilots / Flight crew during boarding?
Mostly you wouldn't need to ask. Most commercial flights use the airline's standard call sign and the flight number printed on your ticket. Sometimes the call sign can be confusing - British Airways use 'Speedbird'; PAN AM used to use 'Clipper'. There's a list of common callsigns on http://www.pilotcareercenter.com/Search-Air-Carrier-By-Name-Region-Aircraft-Type-Radio-Callsign#callsign

The flight number should be enough - just listening for calls referring to 'two-two-zero' will almost certainly identify United 220. Code-sharing flights, however, will generally use the flight number of the operating airline. Your ticket might say 'United 220', but if the flight is operated by, say,  American Airlines so the call sign might be 'American 406'.

All that said, if you're using your phone when you have been explicitly asked to turn it off the airline is within its rights to confiscate your phone or remove you from the flight.