Dear Student,
To your information domicile certificate is necessary for state counselling in most of the states but there are some states where it is not mandatory given that you have sufficient proofs like marksheet of 10th and 12th. Domicile certificate is issued only for the state where you have permanent residence and not for any you reside in. Do search online to check if it is mandatory to have a domicile certificate for state counselling in your state or not.
Hope this might help you.

In most states the domicile is compulsory for counselling.
However, in some states like Maharashtra it may not be mandatory.
You can cross check with the requirement list of the procedure.

No there is no need.....