1) Congress cannot investigate anyone or anybody. Only the Investigative arm of the Government can investigate someone.
2) They cannot or should not hold hearings. Only a court or a Grand Jury can.
3) They cannot make appointments to Federal Jobs. all jobs sjould be applied for through the US Personnel Commission or through the particular Agency Personnel Department.
4) They cannot issue or rule on Pardons. All pardons are either through the US Probation and Parole Department or by Petitioning the President on approved applications.
5) They cannot put their own version of the budget into play without the advice and consent of the person submitting the budget.
6)They can't regulate war time policy. Only the Defense Despartmetn and the President in coordination with the JOInt Chiefs of Staff. Then the rules/polcy is presented then to Congress for approval.
7) They can only call forth the Militia.
8) They cannot commission any body in the military or call up anybody to active duty. The President is the only one that can call up a soldier in the time of war or when the soldiers expertise is needed for a specific task or duty.
9) Congress cannot disapprove or overrride a Preidential veto. When a President vetoes something it is vetoed and only he can rewrite the vetoed measure for Congress to revote on it for his approval and signature.
10) They cannot propose impeachment of a President for non-treasonable crimes. The President has immunity from Prosecution. Treasonable Crimes are those that violate his oath of office.
11) Congress cannot put themselves in the military or give theirr names to somebody to pose as them. They cannot enter Governmental Office buildings or their own office building without presentation of their Congressional ID Card.
12) They are laible for all laws of the Nation, the States of the Union and of the State and Governmental municipalities at which their District Office is located.
These enumerations are what I believe or feel that the Congress shouldn't have any right to preform or get involved in. These items have come from my personal experience in dealing with five Members of the exclusive club known as the US Congress.