Do we need a domicile certificate for admission in classXI or for Engineering, and if yes, what is required to obtain a domicile certificate

Actually it is not required nowadays bcz in u r Leaving certificate it is also written that u r nationality is Indian Domicile is only required for identify u r nationality ok u will got domicile certificate in Setu Suvidha

Some insitutions demand it. You can get the same form the district administration office of your city. If you are not residing at a place which is a district headquarter, then you may approah 'Tehsildaar' of the place to get the domicile certificate.