Reply to first question: Provision for Anticipatory Bail is under Section 438 of the Criminal Procedure Code, the relevant part of the Section reads as "Where any person has reason to believe that he may be arrested on accusation of having committed a non-bailable offence, he may apply to the High Court or the Court of Session for direction under this section that in the event of such arrest he shall be released on bail....."
Applying for anticipatory bail, before filing of FIR, is like a double edged weapon. Where anticipatory bail is sought before filing of FIR, in many cases relief may not be granted. Thus it is advisable not to apply for anticipatory bail, before any FIR has been lodged.
Yes, of course, once FIR is lodged against a person, such person must immediately apply for bail.
Reply to second question: After the FIR is lodged, the police has the power to investigate the case, which includes the power to take measures for the discovery and arrest of the offender.
Reply to next question: If an FIR is lodged against any person(s) specifically stating the offence of S. 498 A, the police has the powers to immediately arrest all or any of the persons named in the FIR, since it is a cognizable offence.
Reply to next question: Section 57of Cr.P.C. clearly mentions that person who is arrested without a warrant shall not be detained in custody for a period of more than 24 hours. Such person has to be produced before the Magistrate within a period of 24 hours. Any detention of such person beyond 24 hours will be illegal.
Thus even if the arrest is made on a Friday, or Saturday or on any other day, even if it is a holiday, the arrested person will have to be produced before the Magistrate within 24 hours of the arrest. Certain Magistrates are made to sit even on holidays, and in an extreme situation, the arrested person may be produced even at the house of the Magistrate. So what your father-in-law says that you will have to spend the whole weekend in the jail, is just to scare you, and put you under pressure, it is totally incorrect.