A bill is a document that needs to be approved by the house, senate, and ultimately the President in order to become a law. In short: It is a not yet approved law.
He believed that by paying Mexico's debt to America would let him have the settlements that he wanted to get the Rio Grande, pay the debt settlement of Mexico in exchange for his conditions, and by California and Mexico as well. Polk thought that since there is a tension between America and Mexico it was best to get in and open some agreements.
The construction of the United States railroads and the growth of US cities after the War of 1812 showed that the American economy grew quickly after the war. It shows that despite the economic crisis that the country went through during the war, it wasn't difficult for them to recover.
Assuming you're referring to the time period around the final days of Rome, one of the most popular forms of entertainment was the "circus", since this could entertain large groups of people at the same time.
It took 60 years as the westward expansion took place from 1801-1861.
