Does the president's executive power extend to removing an appointed official, even if the appointment required Senate confirmation?
The power of the president of the United States does indeed extend to the point where he (or someday she) has the power to remove government officials even if the advice and consent of the Senate is required for those officials to be appointed. This principle was established explicitly by the Supreme Court in the case of Myers v. United States.
The principle of checks and balances does give the Senate the right to approve many presidential appointments. This is so that the president cannot simply appoint whoever he wants regardless of their qualifications or the opinions of the Congress. However, the idea of separation of powers means that the Senate cannot have too much power over the executive branch. In this case, it means that allowing the Senate to force the president to keep a given person in a position would give the Senate too much power over the president.
We can see this principle at work in current events. When General David Petraeus was nominated as the head of the CIA he had to be confirmed by the Senate. When he resigned recently, his resignation only had to be accepted by the president and no hearing by the Senate was needed.