Final answer:
The statement about Britain gaining valuable territory after the Seven Years' War is true. Conversely, the claim that most Indian tribes supported the British is false, as many remained hostile. Also, the war did foster a greater sense of identity among the colonists, which is true.
Step-by-step explanation:
The statement "The most obvious result of the Seven Years' War was territorial changes in which Britain gained the most valuable territory." is true. The Treaty of Paris of 1763 concluded the Seven Years' War, awarding Great Britain vast territories including everything east of the Mississippi River, Spanish Florida, and more; making Britain the dominant European power in eastern North America. However, the territorial changes did not come without consequences, as France's Indian allies protested, asserting France had no right to cede Indian lands to the British.
In terms of Indian support during the period, the statement "Most Indian tribes and nations supported the British because they feared an American victory would mean a greater loss of land through expansion." is false. Many tribes remained hostile to the British following the Treaty of Paris in 1763.
The claim that an increasing sense of common identity among the colonists was one of the legacies of the French and Indian War is true. The war and its aftermath helped to forge a shared experience and grievances among the colonists, setting the stage for future unity in the American Revolution.