How did the battles over New Mexico and California territories give the
U.S. Army an advantage?

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The United States had been not only wealthier, larger, and more populous than Mexico, America also had industries to supply it with arms and ammunition.

to study how the Chinese government operated

to learn about Chinese art and technology

Explanation:

He sent Japanese monks and other men to China to study.  They study mostly how the Chinese government worked as well as art and technology.

He ruled in lat 6th and early 7th century and he made Buddhism the state religion.  He built many temples all over Japan.

Through the messengers he sent to China, he learned a lot and that helped him create a new Japan, making him revered and viewed until today as one of the most important rulers of Japan's history!