Can my wife elegible to ask my bank detail, my salary slip t

she can ask court to produce your salary slip and if you fail to prodcue then if she know the company were you are working she can ask court to issue order to company to produce your documents to court

What about the bank details? Can she ask for the bank detail.
I was occasional send her the cheque from my account so can she know somehow the salary credited from my account? I means to say can count say to me to show my bank detail?

Yes.

I was asked to produce salary slips for the year. In return I asked for her bank statement from inception to prove that I was sending her money regularly. Both requests were sanctioned and ordered by the court.

yes the court can summon the bank to produce provided she gives your account no,Name of the bank and address to the court .

change the salary account to some other bank. If she know your employer she could ask and the court will allow her request.