Regarding manifest destiny, what are examples of peaceful expansion and examples of violent expansion?
For the most part, Manifest Destiny is connected to violent expansion rather than to peaceful expansion. In truth, there was very little, if any, truly peaceful expansion in the history of the United States.
In one sense, you can say that much of America’s expansion was peaceful. At least, it was peaceful with regard to America’s relations with other formal nations. The US got much of its territory in this way. The two main examples of this are the purchase of the Louisiana Territory from France and the treaty with the United Kingdom that gave the US control over the southern part of what was then called the Oregon Territory. The US got these areas without having to fight another country for them.
From this point of view, only the taking of the Southwest from Mexico would be seen as violent expansion. This was the only time that the US fought a war explicitly for the taking of new territory. (You could, however, see the war in the Philippines that arose after the Spanish-American War as such a war.) However, we can also see the expansion into the Louisiana Purchase and the Oregon Territory as violent expansion. While these areas were nominally owned by European countries, they were inhabited by Native Americans. The US had to use violence to remove the Native Americans so that Americans could have the use of the land that they had gotten from the European countries.
Thus, examples of violent and nonviolent expansion depend to some degree on how you define violence.