On 17 June, 1789, Dr. Samuel Bard operated on GW's left thigh. The tumor was very large, and Bard had to excise the infected tissue and pus. It was an enormously painful procedure, but GW remained unfailingly courteous. GW was bedridden for weeks, and many wondered if he would ever regain the strength necessary to lead the nation as its first President. By early September, GW told Dr. Bard that the inflammation was almost gone.
President Washington appeared in the Senate twice. The first was to personally ask why one of his appointments was being blocked. The second (and last) time was to inquire (with his Secretary of War, Henry Knox) the status in terms of ratification of a negotiated treaty with the Creek Nation. The Senate obfuscated by referring the proposed treaty to a committee for further study; GW responded by saying "that defeats the whole purpose of my coming here" - Washington never again returned to the U.S. Senate.
From that point on, President Washington sent missives to Congress, notifying them of his decisions. These actions did more to define the Presidency and the conduct of foreign policy than an entire shelf of Supreme Court decisions on the separation of power among the three branches.
(Below: From the 15:12 - 18:57 mark, watch GW in the Senate w/ the Creek Treaty)
Adams was probably a casualty of being identified, by Washington, as the nominal head of the Senate. GW also had a long memory of those that criticized him during the Revolution, and Adams was one of the names at the top of Washington's list. GW believed that criticism was a lack of loyalty, and many people paid a price for what they said about Commander-in-Chief Washington when he was President. Meanwhile, Adams was secretly exasperated by GW's success and prestige as President; John Adams' greatest fear was that Washington and Franklin would dwarf him in American History.
Washington set up five departments that were designed to provide advice: Treasury, War, State, Attorney General, and Postmaster General. With the Constitution mum about Presidential advisors, GW created the first Cabinet (not pictured; the Postmaster General, Samuel Osgood); by doing so, he created a major shift from Legislative to Executive (in effect, he found another way to bypass Congress). Jefferson viewed the first Cabinet as a wheel, with Washington as the hub, and the others as the spokes . . . but those spokes featured an incredible array of talented young (relative to GW) men.
For the crucial position of Secretary of State, GW offered the post first to John Jay, but Jay had his eye on being the first Chief Justice of the Supreme Court. GW then "settled" for someone he knew from his days in the Virginia Assembly: Thomas Jefferson. Jefferson took months to decide whether-or-not to accept the position; he took so long that both GW and James Madison had to pressure him hasten his decision (to accept!).
Hamilton practically burst through the doors of the Treasury Department with sky-high enthusiasm and a desire to do his best to make the new federal government a long-term success. Jefferson, on the other hand, was not very enthusiastic in carrying out his duties as the first SecState. A possible reason for his delay for accepting the post, and his lack of energy in heading State was that he wasn't very comfortable with the federal government as envisioned, written, and ratified.
The Attorney General was Edmund Randolph (pictured; he was only 36), and he was frustrated in that he really didn't have a department to run like the others . . . it was basically GW and him. Randolph had so little to do that he actually took private clients as a lawyer.
There was high turnover in the early years of the Supreme Court under the Constitution; "Riding the Circuit" was the main reason. Supreme Court justices spent a long time away from the comforts of home, and also had to endure miserable working conditions and substandard lodging. The lack of prestige alone lead to resignations and a low-level of interest in serving on the Court. GW would appoint 11 justices to the Supreme Court (in the early decades, there were only 6 justices) . . . the Supreme Court was an institution searching for a mission.
For example, Washington deliberated quite a while on the pros and cons of the proposed
Bill of Rights; he then actually changed his previous stance in opposition to adding amendments to the Constitution. GW's open support of the Bill of Rights broke the logjam in Congress in terms of their proposal for ratification.