senate
The Senate has the power to confirm federal judge appointments made by the president. The president nominates the judges, but their appointment must be confirmed by a majority vote in the Senate before they can assume their positions on the federal bench.
If the new president died, the vice president would become the president. He then would nominate someone to be his vice-president and ask Congress to confirm his choice. If Congress rejects his choice, he chooses someone else until he finds someone they will confirm.
The electoral college that elects the president also elects the vice president. In the event that a new vice president is appointed because of a vacancy, both houses of Congress have to confirm the president's appointee.
Congress has the ability to overrule the President's veto power with a 2/3 majority vote. Furthermore, Congress has the power to impeach the President, and must confirm the President's choices (i.e. appointment of the Supreme Court, etc.). Congress checks the Supreme Court in a few ways as well. First of all, it has to confirm the President's appointments of Supreme Court judges. It also has the power, once again, of impeachment, and has the ability to amend the Constitution.
Vice presidential vacancies are to be filled by the President and confirmed by Congress.
The Legislative Branch; U.S. Congress.
No, state judges are either elected or appointed.
The President doesn't need anyone's approval to select, or nominate, a Federal judge, but the judge can only be appointed with the "advice and consent" of the Senate, which is only one chamber of Congress. Appointment requires a simple majority (51%) of the Senators voting. The House of Representatives, which is the other chamber of Congress, plays no role in this process.
Congress
This would essentially put the supreme court under the president and let him decide the constitutionality of laws if Congress agreed with him. However if the opposition controlled Congress, the president might fire the whole court and Congress might refuse to confirm his new appointments and chaos would result.
the president appoints them and the congress questions them
There are many ways Congress sought to limit the power of the executive branch. These are as follows: 1) Congress can override the veto of the president; 2) Congress can refuse to confirm presidential appointments; 3) Congress can impeach the president; 4) Congress can refuse to ratify presidential treaties.
The U.S. Constitution, Amendment XXV, Section 2 states, "Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress."