for part (a), (1), in the answers I am confused about the working s about why the depreciation was added to the net profit and also the head office cost.
The question specifically says that the ROI is to be calculated using the controllable profit (as is usually the case for the ROI). The depreciation and the head office costs are controlled by the head office and not by the division.
The division has no control over head office costs. The head office controls the costs in the head office and can charge the division however much it wants to.