Why did Hamilton support the U.S. Constitution?
He supported it because he thought it was the best system that could be devised, although it was a throng of compromises and he wished the government were stronger. Since Hamilton couldn't stand the government under the Articles and thought the Constitution was better than anything else, he fought tirelessly for it, braving the New York ratifying convention and writing the Federalist Papers.
Yes he did. Hamilton supported a looser interpretation of the Constitution so that the central government could be strengthened at the expense of the state's rights. He believe that the government should be allowed to use the implied powers and the elastic clause from the Constitution to his advantage.
Actually Alexander Hamilton believed that New York City would be the best location for a new capital. It had been briefly before the US Constitution was passed. Hamilton, a founding father, believed that NYC was a logical choice because of its size, its reputation as an international city and because business and finance was established there.