Nobody.
We should make up our minds. All the questions you raised are interesting. Do we want the ombudsman to report to the House or to a committee? Do we want him or her to be a kind of auditor general? To we want the ombudsman to report to the department?
That is the first point that should be settled. After that, we will be able to answer all the interesting and relevant questions you asked. But first of all, the House needs to create this ombudsman position and determine its mandate through a bill instead of merely giving directives to the department.