Did the quest for “self-rule” change from 1700–1900? How (in what ways, by what means) and how not (that is, what has remained unchanged), and what explains the change or lack of change?

Self-rule, like independence, is a relative term. If we look at both Europe and what is now known as the Middle East in the year 1700, we can see that there were multi-ethnic states within which one national group held power over other groups, states in which power was held by outsiders, and states in which, regardless of the issue of ethnicity, power was held by a monarch or an oligarchy (a small group of ruling elites) and denied to the population at large.
However, in 1700, few people were actively complaining about this situation or demanding fundamental changes. In England, more than any other European country, a democracy of sorts already had been created, but it was a democracy only in a relative sense, based on a Constitutional system that had developed gradually over centuries, the latest phase of which had begun with the "Glorious Revolution" of 1688.
100 years later, by 1800, it was a different story. Both the American and French Revolutions had occurred, overthrowing, in the first case, power held by an outside oligarchy (the British government) over its colonial offshoot, and in the second, power held by a monarchy over its own people.
What had caused the quest for self-rule? The answer is enormously complex, but to try to sum it up in one sentence, I would say that various factors (beginning well before 1700) had changed the way people viewed themselves in relation to each other and in relation to both the government and the religious authorities.
By 1800, few people believed that monarchs ruled by "divine right." Moreover, just as the view of people in relation to each other individually and to their governments had changed in favor of an egalitarian philosophy, that same idea of equality began to be applied to different ethnic or national groups. In 1800, the Slavic nationalities, the Hungarians, the Greeks, and several other ethnic groups did not rule their own countries. Ethnic self-determination became a huge factor in nineteenth-century political thought. Over the course of the century and continuing up to the end of World War I in 1918, the Austrian and Ottoman empires were dissolved, and new countries were formed in Europe and the Mediterranean in which national groups now ruled themselves.
Therefore, over the course of a 200+ year period, authoritarian governments had been replaced by democracies, however imperfect, in the form of republics or constitutional monarchies, and people were no longer controlled by rulers from outside their ethnic group. This, of course, was only true of part of the world. At the same time that Europeans had liberalized their own continent, they had been busy taking over other people's in Asia and Africa. In 1900 those same ideals of self-rule that had animated Europeans were felt by people everywhere. It took at least another half century for self-rule to be realized throughout the world.