Yes, HDFC Addon cards don't report to cibil; primary cardholder is billed for entire charges and is solely responsible. So anyone (as long as their identity can be verified) of any age can be Addon cardholder for HDFC
Did you have e-statements enabled? If yes, you should have got an email with pdf statement within 2 days of the statement date.
Netbanking>>Cards>>Enquire>>View Statement rarely work for me. Always throw errors.
Maybe call customer care and ask?
Regardless I am sure you will get a letter...
If you are looking for status miles (and not just award miles) - you may look into Egypt Air. MS allows pooled status for the primary account holder (family head). Having said that redemptions are not easy as it involves contacting MS redemption desk via phone/email. So YMMV