As I understand the AB application does not go to PS . It is simply filed in Court and Court will give a date on which it will be heard and dispose off your application i.e will grant bail or reject. As in your case you are aniticipating case like 498A, DV and they are not filed yet your lawyer will have to argue well and provide reasons for you seeking anticipatory bail including all the anticipated cases . If sessions court rejects then you have option to go to High court else if it fails in SC you can go to High court.
If you really feel things are bad and cases could be filed against you , it's better you take AB for you and immediate family members. It's worth the expense rather than facing hassles later . Trust my words.
The AB validity is till the end of trial in a scenario where cases are filed . If case is not yet filed Court may impose some validity condition but I am not sure about it. Don't worry if there is any validity your bail order will have it mentioned explicitly . In any case you needn't worry about Police once you have AB order from Court as the rest is just formality. Police cannot arrest you. if a case is filed against you then you can show bail order to police , they will enter in their records an arrest and released thing . Your lawyer will do it on your behalf . So no worries.
For your reference read Section 438 Criminal Procedure Code ( Cr.PC) .Just google it.It speaks about Anticipatory bail.
Now answering your questions specifically.
1) How many days does it take to get the Anticipatory Bail in the Civil Sessions court?
Ans : It may take a day or two as Kapil Sir has mentioned or more like even a month depending upon when a case is scheduled for hearing. Even sometimes High Courts hear it after a month. Nonetheless bail application being a matter related to Personal liberty of an individual is given importance.
Note : 1 month was my personal experience hence mentioned it . Lawyers in this forum are the experts to give you rough idea on the timelines.
2) Does the court need any permission/inquiry from Police to give anticipatory bail?
Ans : Court may inquire from Police if they want something but no permission.Courts , magistrates and Judges are way above than Police. If they feel bail should be given it will be given.
3) What is the usual validity period for Anticipatory Bail.
Ans : Already in the above text.
does the AB application goes to the police station and takes much time to get response from there PS?
Ans : Where cases are filed already , Courts seek CASE DIARY from Police before deciding on Bail order. Remember Case Diary is confidential to Police and Courts . Your Advocate can also see it but it will never be disclosed to you.
If case is not filed yet no point in enquiring from Police. Remember AB is purely a Court matter and application will not go anywhere else.Judge will decide on merits and accordingly decide your bail application.
Tell your lawyer to speeden up things .