If all the details are correct, the funds will appear in your WazirX balance within 6 hours on working days. If you deposit after 9 PM or on weekends, then it will be done on the next working day.

About your second query, you can't fund your WazirX account using a bank account that is not in your name. WazirX requires the bank account and WazirX account name to be the same; this will prevent you from any kind of fraud.