Does Court Have An Organizational Structure?

Yes courts and tribunals do have an organisational structure like most organizations, to enable them to function efficiently.

I will answer this question with regard to the British Legal system.There is the court then the High Court or Supreme Court as it called in some countries.This has the final say in certain matters.Family matters of access and adoption of children and the like, are heard in the High Court, in addition to serious criminal cases, and necessitate lawyers, advocates and specialist Judges. who rank in the order in which they have been given.

Lawyers generally consult directly with the client or family, and then advise the advocate who has his area of expertise, and then the matter is heard before the judge who is advised  on the case by the advocate. The tile of QC is used in U.K. and is a specialised legal professional.

Of course there are the lower courts which hear matters like financial disputes and these can have a magistrate who acts as judge. In the U.K. there is the small claims court where contested matters of dispute, involving sums of money under the limit of £5,000 pounds are heard. Without the legal costs associated with other courts, and the necessity of having a legal representative like a lawyer.
This is a short simplified version of  how the court system is constructed.