How did the politics of Andrew Jackson, Manifest Destiny, and Westward Expansion impact the Cherokee, Mexican, and Chinese populations? What societal and/or legal obstacles did each of these groups face in attempting to assert their rights?

Andrew Jackson had his greatest impact on the Cherokee population, pushing them and other southeastern tribes off their land with his Indian Removal Act. The Indian Removal Act was a key part of Jackson's legacy, as it gave land to his Western constituents and directly led to the Trail of Tears, on which thousands of Cherokee died.
While Jackson did not annex the Republic of Texas, he did not discourage Americans from moving to Texas as guests of Mexico, but he later supported their freedom from Mexican laws. As a retired politician, Jackson would go on to suggest to one of his proteges, President James Polk, that it was in the United States' best interest to annex the young republic.
Under the doctrine of Manifest Destiny, Americans believed that it was their God-given right to spread their culture and governance over the entire continent. This notion became popular in the early 1840s, after Jackson had finished his presidency. One of the major events tied to Manifest Destiny was the Mexican War, where the United States severely defeated the Mexican army and took much of what would become the Western United States. While part of the treaty ending the war stipulated that Mexicans living in this conquered territory would be treated fairly, this was often not the case, as Mexicans were faced with discrimination from encroaching whites.
After the discovery of gold at Sutter's Mill, people came from all over the world to get in on the California gold rush. Many Chinese people came as well, taking on abandoned gold claims and making a modest living off gold pieces considered too small to maintain white prospectors's attention.
Upon hearing that Chinese immigrants were successful, the white prospectors looked both to the courts and to extralegal methods in order to get back their claims. When Chinese immigrants took to selling things to the miners, the miners claimed that they were taking away jobs. All of the protests against Chinese immigration would ultimately lead to the Chinese Exclusion Act, passed under the leadership of Rutherford B. Hayes. It was the first attempt to limit immigration into the United States.

Starting with the Louisiana Purchase, America began a new era of westward expansion. Unfortunately, due to the doctrine of manifest destiny—which seeped into popular consciousness through foreign policy throughout the nineteenth century—US leaders like Andrew Jackson made aggressive territorial acquisitions that often ignored the legal rights of Mexican, Cherokee, and Chinese populations.
Jackson ignored the land rights of southern Native American tribes by repeatedly drawing up new treatises that forced relocation. The infamous Trail of Tears tragedy following the Five Civilized Tribes' exodus as enforced by the Indian Removal Act is a direct result of Jackson's policy. In addition to the deaths of thousands of Native Americans, Jackson's administration eradicated tribes' cultures, languages, and traditions.
Jackson impacted Mexican populations with his adamant insistence on annexing Texas. By ignoring the territorial claims of the Mexican people, Jackson would start an order that culminated in the bloody Spanish-American War. The war resulted in the suppression of Mexican culture, and thousands of the Mexican Texas population suddenly found themselves without citizenship.
The Chinese people suffered indirectly from the legacy of Jackson's continental expansion. When Chinese immigrants began moving to California in the mid-1800s, they tried to own land and businesses—a fact that angered the local white population. Lynch mobs and white terror groups intimated the Chinese into giving up their land. This coercion had a lasting impact on Chinese-American society because immigrants were forced into specific industries: hard railroad labor, restaurants, and dry cleaning.