Thank you For your reply. I have the approval add-on installed. but again what level of permissions shall I give to the group manage? 

By going to my team>>choose the manager>>permissions, there are a set of 4 permissions:

1- Admin

2- payroll Manage

3- Custom

4- Worker

Which one of those should be the group manager in order to let him be able to approve ONLY this group members' timesheets and PTO's (not all the team members aka emplyees) and making sure that he is not able to see the employee data (salary,,,etc)?