1) you have to make application to court to change date of birth in your passport
2) enclose your birth certificate which mention correct place of birth . also enclose copy of your passport
3) your personal presence would be necessary for filing application
4) you can execute POA in favour of family member to be present on various dates
5) it should take around 6 months
6) legal fees vary depending upon lawyer engaged by you
7) application can be filed in hyderabad as you are residing in Hyderabad and passport issued from Hyderabad