No, not technically...... however it could be considered one when it is called together to vote on the possible impeachment of a President.
Senate
The senate does.
The Senate confirms both federal judges and Supreme Court justices.
Presidential nominations of federal court judges are made with the "advice and consent" of the Senate, just as Supreme Court nominations are. The Senate must confirm the nomination by a simple majority of those voting in order for the judge to be commissioned.
The supreme court is the highest federal court and has the final say. Their role of the supreme court is to interpret the constitution
senate
senate
In Australia, the difference between these to institutions is that the High Court of Australia. Deals with Constitutional, Discrimination, Homicide Cases, and other cases which are seemingly have a superior need to be heard in front of a court. The senate deals with democratic issues such as passing or rejecting legislation. For example, the 'Carbon Tax' issue or the 'Plain Packaging' on Cigarette Packets. In summary, the High Court is to hear issues that comply with the constitution and the Senate deals with democratic issues. Which in this case the High Court and the Senate are very similar, however, it is evident that The High Court is superior over every other court in the 'Australian Court Hierarchy' (Local Court, District Court, Supreme Court, Federal Court and The High Court). And The Senate is superior over all democratic government (House of Representatives, Federal Government, The Senate). Therefore, the Senate is not a 'Court'. Therefore to answer the question, The High Court is superior.
senate
Yes and no. Federal officials and elected representatives CAN be prosecuted in a court of laws, but the President can only be impeached and then tried by the Senate.
The President appoints federal judges and the appointments are approved by the Senate in Congress.
Senate approval of nominations to the supreme court