Yup, it is full recovery. The second db should be in high availability as production db is running 24x7 and every minutes day and night data will be coming in....

If I would to use Full or Simple Recovery mode, would it makes any differences? the full backup incurs during Saturday and Sunday evening, the differential backup incurs during Monday...

Thanks Gail for the help. Would the transaction logs increase in size if I decides to run the Backup process on the DB?