Final answer:
The true statements are 2, 3, 5, 7, and 8, regarding the conditions for settlers in Texas, Santa Anna's centralization of power, the brief independence of California, America's attempt to purchase land from Mexico, and the future Civil War generals who served in the Mexican-American War.
Step-by-step explanation:
1. False. The statement is false because while Americans did move into Mexican territory, the Mexican government initially permitted American immigration under certain conditions.
2. True. Stephen A. Austin and settlers were expected to convert to Catholicism, learn Spanish, and comply with Mexican laws, including the prohibition of slavery.
3. True. In 1835, Santa Anna attempted to centralize control in Mexico, impacting Texas right to self-governance and contributing to the rebellion.
4. False. Texans did wish to maintain their independence after the rebellion but were eventually annexed by the U.S. with the support of many Texans.
5. True. California was briefly an independent republic before being added to the U.S. as part of the Mexican Cession.
6. False. It was President James K. Polk who asked Congress for a declaration of war, not John Tyler.
7. True. America initially sought to purchase California and New Mexico from Mexico, but after the war acquired more territory for $15 million.
8. True. Many men who fought in the Mexican-American War became prominent generals in the Civil War.