Legislative Context
The Inquiry has been established under the Inquiries Act 2005 (“the 2005 Act”) and is subject to Rules made under that Act and related provisions.
The Inquiries Act 2005
The Inquiries Act 2005 gives Ministers the power to set up a public inquiry where events have caused or are capable of causing public concern, or there is public concern that particular events may have occurred.
The Act sets out how an inquiry is established, and various matters to do with its proceedings, such as the role of an inquiry panel (which may, as here, be a chairman alone), the relevance of an inquiry’s setting-up date, evidence and procedure, access to the inquiry and the inquiry report.
The Act is here:
The Purpose of an Inquiry
Within the confines of its terms of reference, the purpose of a public inquiry is to investigate thoroughly the matters in question to establish the facts and to find out what happened. Where necessary, recommendations will be made to prevent something from happening again.
By statute, an inquiry cannot determine civil or criminal liability, or award compensation. However it is not to be inhibited in the discharge of its functions by any likelihood of liability being inferred from facts that it determines or recommendations that it makes.
An inquiry is often described as “inquisitorial” as compared to the “adversarial” proceedings in a court case. It is a means of seeking out the facts in a way that would not be possible in adversarial proceedings in which one party wins and another loses. A public inquiry does not decide in favour of one side or the other, nor is it a trial or a disciplinary hearing.
There will be some people who have evidence to give to an Inquiry and others who may have a legitimate interest in challenging such evidence. However, from the Inquiry's point of view there are no parties or sides.
An Inquiry relies on the co-operation of individuals and organisations to assist it. However, it does have the power to call witnesses and to compel witnesses to give evidence, either in writing or orally, and to produce any relevant documents.
The Inquiries (Scotland) Rules 2007
The Rules, which came into force on 19 January 2008, were made by Scottish Ministers in exercise of powers under the Inquiries Act 2005. They deal with many points of detail about how an inquiry under the Act is conducted. These include provision about core participants, recognised legal representatives, evidence, and witness expenses.
The Rules are here:
Determinations
Under the Inquiries Act 2005 Ministers have power to make determinations about various matters. Scottish Ministers have made a determination about the chairman’s power under the Act to make awards concerning legal representation.
The Determination was announced by way of an Answer to a Parliamentary Question and is here: 
Awards concerning legal representation (PDF, 23Kb)
Conduct of the Inquiry
Subject to the provisions of the Act and Rules, the procedure and conduct of an inquiry are for the the chairman of the inquiry to direct.
Note
The links above are to the original versions of the 2005 Act and the 2007 Rules as provided by the ‘Legislation’ section of the Office of Public Sector Information. If you wish to check whether there have been any changes to the Act, or the Rules, you must use a website offering that functionality, such as Westlaw, or Lawtel.