Can i file non-cognizable complaint directly in court

Yes! You can file noncognizable offence/complaint of Blackmail ansd criminal intimidation directly before the court.

Yes, you can file a private complaint directly in Judicial First Class Magistrate's Court.  Before filing directly in the court try going to the Police Station with your complaint and obtain acknowledgement.  If police does not register the case, then go to court along with the proof. 

Agrieved person can directly file a petition for non-cognisable offence in the courts only. FIR cannot be registered without magistrate’s permission

Dear Qutubuddin,

                                  Please primarliy send a complaint by registered post with AD to The Station House Officer & The Concerned Assistant Commisioner Of Police,  & once you recieve the AD card please approach the concerned jurisdictional magistrate and file a petition of Private complaint under sections 190 & 200 , seeking a direction either to the concerned police station or asking the Hon'ble court to take cognbizance of the said offences.