Does the BankID AML service tell which customers I should approve and not?

No, it is the one required to report that know the customer and that need to consider whether a customer relationship can be established or not based on a risk assessment. 

BankID AML offers support in this assessment in the form of structured quality data, but it is eventually the one required to reports' responsibility. 

What the law refers to as "outsourcing of customer control" is not included in this service.