(1) I am sorry to say that the chats were some erotic/love affair kind of. I have no recent such evidence of their act. Can I file divorce on mental cruelty/adultery? Can her ex-boyfriend be summoned to court to testify?
If you have some clinching evidences to prove her adulterous life then you may implead that person (her paramour) also as a respondent in the divorce case filed against her on the grounds of adultery otherwise you ca file divorce on mental cruelty alone in which you can include such events in the pleadings.
(2) Can my wife sue against me for breach of her privacy even if I am her husband on the ground of accessing her mail account without knowledge?
Yes she can very well go ahead, she has got rights for her privacy and can take anyone into task is found to have invaded into her privacy.
(3) I am confused that if it is illegal as it is a breach of her privacy to access her mail chats using her password without her knowledge/consent then how those chats can be regarded as evidence in the court of law?
Who said such things can be taken as evidence in court, you have to prove your allegations properly and not by producing any such fabricate documents, because court will consider them as fabricate documents only.
(4) When voice call records are not retrievable, then Is it possible to get a court order to reveal the call data record (CDR) of her mobile for last two years (postpaid SIM no. is in her name) for the Reliance Communications no. she is using?
You may file a petition before curt to send for the records from the concerned authority which are vital to your case.
(5) Is it easier to get through such a court order for CDR or any private detective agency can access it easily?
Private detective agency will b able to it easily and not court.