The answers to all of these questions are closely connected to one another. The state of Germany after WWI helped lead to the rise of the Nazi Party. The Nazis were able to rise in part because of their foreign and domestic policies.
First, however, we must note that the Nazi Party did not come to power immediately after WWI. As late as 1928, the Nazi Party got less than 3% of the vote in a nationwide election. It was really the Great Depression, as much as WWI, that allowed the Nazis to take power.
In the years soon after WWI, Germany was in bad shape. Perhaps most famously, the country’s economy collapsed so badly that hyperinflation occurred. This made money essentially worthless and made it very difficult for the economy to function. This, of course, led to political turmoil. People in the country were also upset about the Treaty of Versailles. They felt that it treated Germany unfairly. Thus, they wanted both economic reconstruction and a foreign policy that would restore their sense of pride and Germany’s position as a major power in Europe.
The Nazis came to power in 1933. Between the early 1920s and 1933, Germany’s economy and politics had improved under the rule of Gustav Stresemann. This made Germans relatively content so they were not likely to support radical political parties like the Nazis. When the Great Depression hit, however, the economy went bad again and the Nazis gained support. This culminated with Hitler being named chancellor of Germany. (He was not voted in as chancellor by the people. Instead, he was selected by political leaders who hoped to benefit from Nazi popularity.)
The Nazis improved the German economy largely through public works and a more aggressive foreign policy. The government built canals and highways. It started to build a lot of weapons because it wanted to be more aggressive in its foreign policy. By being stronger and more aggressive, it hoped to regain Germany’s position as a major power and, hopefully, to regain much of the land that Germany had lost in WWI.