Presumably he was rather busy as Commander-in-Chief of the Continental Army, a position to which he was appointed in June, 1775. The fighting was underway well before the Declaration of Independence was signed in July (or August, or November, depending on who you ask) of 1776. The battles of Lexington and Concord in April, 1775 are usually considered to mark the beginning of the war.
False. Mexico was already independent. The settlers, largely from Tennessee, came in order to support the Texas independence movement. Not Mexican independence from Spain.
Native American customs were being outlawed by state governments in the United States.
