Michael:
1. For transaction purposes (what is shown in WIP, and how it shows in cost aggregations), the transactions for Test op 2 will inherit the cost type of the parent task, and be classified as Operating. The Cost Type field on the Test op 2 task will remain blank, as it is not necessary to fill that field to establish inheritance.
2. The UI does not populate the child task Cost Type field from the parent value.
3. Reports that show the Task attributes, such as the one you included will have the Cost Type field blank. You will need to look at the value in the parent Task to see what the implied value is for the child tasks. Reports that show Costs associated with transactions (or planned costs) will show the cost type that is inherited from the parent task - Operating in your use case.
Where you absolutely need to see the explicit value of the Cost Type at the child task level based on the value in the Parent Task, you can use a workflow process to populate any Child Task's Cost Type that is blank with the value of the Parent Task Cost Type.