Lets say I do a full backup January 1st. Then I do incremental backups every day for the week and then a new full backup on January 7th and then incremental backups for that next week and do another full backup on January 14th. Now, can I safely delete the full and incremental backups from the week of January 1st till January 6th?
Yes, you can.
This can also be achieved automatically in CB by using macro feature in backup step 3 with the option to reset the macro every 7 runs.