A) What happened in 1929-32 which led to the Nazis becoming the most popular political party in Germany?.
In 1929, Germany was a in a turbulent state. Due to proportional representation (PR) no party could solely form a government. The large governments had to work with smaller ones in a 'coalition' government. This is obviously a problem, because these parties could never really compromise on a decision. The five parties active then, therefore, were not successful at what each of them were trying to achieve. Article 48 of the German Constitution allowed the President to pass laws without the Reichstag having to have to vote. The President (Hindenburg) appointed Bruning to form a new government (without the Social Democrats). He cut government expenditure to overcome depression, but this wasn't a popular move. After another election, the Nazi Party grew from a mere 12 seats to 107 seats in the Reichstag. Next, the Nazi party spent a lot of propaganda to double its votes by 1932. By then, they were the strongest ever party. .
B) Why was Hitler asked to be a chancellor in January 1933?.
The early 30s saw President Hindenburg and chancellor Bruning ruling by decree. This meant they were making decisions by themselves without consulting the Reichstag (which was the democratic body). Arcticle 48 of the German Constitution allowed the President to do this legally, but this meant democracy was being sacrificed. Bruning's way of slashing Government expenses made him very unpopular. Schleicher (a senior armany personell) suggested and made sure Bruning was fired. Franz von Papen was appointed chancellor, but he was not popular either.
A series of elections only saw a decline in his popularity and after being voted 'no-confidence' was sacked as chancellor. Papen suggested absolute control (ruling by decree) but Schleicher warned against it took his place. After the Reichstag wouldn't agree to his decisions and Hindenburg fired him (after he suggested ruling by decree, something he had previously warned about).
