FIR stands for First Information Report. Whenever anybody reports about any crime which discloses commission of a cognizable offence then information is entered into a register whose performa is as per form no – 24.5 ( I ) of Punjab Police Rule.
It is the right of complainant to get an FIR registered if his complaint discloses commission of any cognizable offence. It is the right of the complainant to get one copy of FIR free of cost, immediately from concerned police station. FIR can be registered either on written statement or verbal statement of complainant which is later reduced in writing by Police Officer and is signed by the complainant.

If your complaint does not disclose any offence or your complaint discloses only non-cognizable offence, then FIR cannot be registered. In such cases where only non-cognizable offence is made out, Police officer will enter the substance of information in the general diary of Police Station and give copy of the same to complainant. Another copy of complaint is sent to the concerned Judicial magistrate for further action. Police does not have powers to investigate a non-cognizable offence without the orders of the magistrate.

Cognizable offence :- An offence for which a police officer has the powers to arrest without a warrant is defined as a cognizable offence. Offences like murder, rape ,kidnapping , theft , robbery , fraud etc. are classified as cognizable. To get detailed list of cognizable offence kindly refer to first schedule of Criminal Procedure Code.
Non cognizable offence :- An offence for which a police officer does not have the power to arrest the accused without warrant. To get detailed list of non-cognizable offences please refer to first schedule of Criminal Procedure Code.

Bailable Offences are those offences where the accused has the right to get himself released on bail after his arrest if he can give sureties or personal bond to the satisfaction of the police officer. For the list of bailable offences please refer to first schedule of Criminal Procedure Code.
Non-bailable offences are such offences where the police does not have the power to release the arrested person on bail (except under certain special circumstances ) . The arrested person is to be produced before the judicial magistrate within 24 hours of the arrest .For the list of non-bailable offences please refer to first schedule of Criminal Procedure Code.

Yes, a police officer can arrest a person without warrant if he has been involved in any conizable offence.

Yes, a police officer can search for the person / place without search warrant under certain conditions.