How we cite our quotes: (Paragraph.Sentence)
Quote #1
I constantly hoped that it would have been much earlier in my power […] to return to that retirement from which I had been reluctantly drawn […] but mature reflection on the then perplexed and critical posture of our affairs with foreign nations, and the unanimous advice of persons entitled to my confidence, impelled me to abandon the idea. (3.2-3)
An old trope that you see in a lot of gangster movies is "as soon as I think I'm out, they pull me back in!" Washington's version is similar—he wanted to get out of the game, but he just couldn't abandon people in their time of need. It's the heroic sacrifice that you also tend to see in a lot of action movies.
Quote #2
With slight shades of difference, you have the same religion, manners, habits, and political principles. You have in a common cause fought and triumphed together; the independence and liberty you possess are the work of joint counsels, and joint efforts of common dangers, sufferings, and successes. (10.4-5)
Washington tries to stress the unity of the nation a lot in the farewell address, which isn't surprising because some serious divisions had started to show themselves during his presidency. Here, he urges the audience to remember that they're not so different as they might think and they should work together using their similarities rather than let divisions tear them apart.
Quote #3
The very idea of the power and the right of the people to establish government presupposes the duty of every individual to obey the established government.
All obstructions to the execution of the laws, all combinations and associations, under whatever plausible character, with the real design to direct, control, counteract, or awe the regular deliberation and action of the constituted authorities, are destructive of this fundamental principle, and of fatal tendency. (16.8-17.1)
The principle Washington is promoting here is basically following the rules. People create the government, and they should therefore follow it, too. Otherwise, they're destroying the system that they themselves built. In other words, they're ruining it for everyone else who did follow the rules.