Does my savings account balance affect my CIBIL score?
No. Your credit score is based purely on your credit-related activity regarding loans and credit cards. Your savings and current account balance or the performance of other investments does not affect your credit score. Neither does your education.
Is it good to have zero credit? (i.e. No loans or credit cards)
No, in fact, not having any loans or credit cards (or having a minimal number of loans) has a detrimental effect on your credit score. Lenders like to see a long repayment history in order to better judge your payment reliability over a period of time. If you do not have a sufficiently long credit history, your credit score will suffer.