A loan rejection does not impact your credit score directly. However, you would have applied for a loan which allows the lender to do a ‘hard pull’ on your credit report. This inquiry is stored in the report and the number of inquiries does have an impact on your credit score.
Similarly, a loan rejection will not necessarily be reflected in your credit report. However, multiple inquiries in quick succession could be perceived as an indicator of risk by some lenders and it will also impact your credit score. A declined education loan should not deter you from applying elsewhere but be sure that you don’t end up applying for multiple loans (credit cards etc.) at once
CIBIL report will be pulled for all signatories (borrower, co-applicant) to the loan agreement. It is not necessary that you have a CIBIL score. If you don’t have a CIBIL score, which is common for a lot of students or new graduates as they might have never used a credit product, your report will return a value outside of the 300-900 range and is treated accordingly by the lender.