Last question should be first, and it's simple: No! Washington would cultivate an air of detached impartiality, especially later when he was in the Constitutional Convention and then President. But that could not really hide a man very much wanting to advance himself and his fortunes. When Washington's ambitions were being thwarted, or his position was threatened, that mask of impartiality and detachment could drop. During the Revolution, in the bad year of 1777 the northern campaigns under Horatio Gates in New York had shown some success but Washington's , in Pennsylvania and New Jersey, had not. An irascible and ambitious Brigadier General, Thomas Conway, wrote a letter critical of Washington to Horatio Gates, and it leaked. The matter was trifling, the possibility that Washington would have actually been replaced was very small, but Washington furiously reacted as though there was an active conspiracy to get the Continental Congress to replace him. Washington's many supporters used the occasion to denounce his critics and show their loyalty, and Gates's blundering responses to this would, in the end, shift him out of command. So, no: he appreciated good officers, like Daniel Morgan, but Washington very much felt he should be in charge.
However, he was right to consider his time in the French and Indian War disappointing. He committed a number of blunders- like, siting Camp Necessity in the bottom of a valley where it could be easily shelled, and then starting a war instead of negotiation. He was also ill, at a time when he was supposed to accompany Braddock. And here his ambition was a problem: in the several occasions when he was in command of a unit and a higher-ranking officer appeared, he accepted their authority only grudgingly. And he was resentful when, after years of struggle with his militias, the large professional army arrived at last to save the day and General Amherst did not give him what he felt to be his due reward of being made a royal officer. He would even appeal that to VA governor Shirley.
But much of Washington's disappointment he could justifiably blame on others. The colonial governments in the early stage of the war were dithering and divided. Their inability to make a proper effort was the reason a professional army finally had to be sent over from England. Washington's militia were very badly supplied and fed, sometimes almost ignored and abandoned. If in later years he wanted to spread the blame for his poor performance, it was easy to do.