Germany was a parliamentary democracy at the time (1932), with both a president and chancellor. The president, who was pretty powerful, was elected, while the chancellor (who was not all that powerful) was chosen by the President, but via allying with the party with the largest number of members in the Reichstag. Because there are a number of parties, not just 2, it is often necessary to form coalitions to get a majority. So, in the German presidential election of 1932 (in March-April), the incumbent president, 84 year old Paul von Hindenburg, won with 53%, and Hitler came in 2nd with 36.8%. Basically the only reason von Hindenburg ran was to defeat Hitler. He was elderly and seriously infirm, but the prevailing opinion of the time was that Hitler would have defeated any other candidate but von Hindenburg. So the presidency was decided and then von Hindenburg chose his chancellor from the Centre Party, with whom he was allied.

Then, in July 1932, there was an election of members of the Reichstag, and this time, the Nazis won the largest number of seats of any party. And again there was an election in November 1932, with the Nazis keeping their position as the largest party. Von Hindenburg didn't like Hitler, but he and his current chancellor again couldn't manage to create a coalition sufficient to overpower the position of the Nazis, and so couldn't create a viable government. So the ailing von Hindenburg, with von Papen's promises of controlling Hitler, was induced to appoint Hitler as chancellor, which was the Nazi's condition for allying with von Hindenburg, while von Hindenburg got the current chancellor, Franz von Papen, to be appointed Vice-Chancellor and his apparent successor, as von Hindenburg knew he would not be living out much more of his 7 year term. While von Hindenburg was alive, the overconfident von Papen tried and mostly failed to keep the Nazis in check, though. The Nazis used every opportunity they could to grab power and to block von Papen from access. The Nazis were uncompromising and aggressive. Hitler used his position to get von Hindenburg to pass various legislation that increased government power and decreased civil liberties. Von Papen resigned in July in protest for these excesses on the part of the Nazis, and then Hindenburg died in August 1934, at which point Hitler declared himself to be the head of state, even though he legally wasn't.

Hitler then held a referendum, also in August 1934. This is likely the second election you are referring to. But it wasn't exactly an election and it wasn't exactly fair. The referendum was on merging the posts of Chancellor (the post Hitler held) and President of Germany (which was vacant following President Hindenburg's death 2 weeks earlier) People were given a ballot that they would write a check on if they wanted Hitler, and leave blank if they didn't want Hitler. You can see how this can open up the possibility of fraud. All someone would have to do is add a check mark to previously blank ballots. You can also see that it wasn't exactly electing Hitler to office. It was expanding the power he already had because he'd seized it. He did win in a huge landslide, receiving almost 100% of the vote in some areas. He was indeed very popular--if there was fraud, it was likely in the attempt to get him closer to 100% support, not to get a majority, which he already had.

So while the Nazis hadn't "won" any of these elections in the sense of Hitler winning and becoming president in 1932, or the Nazis getting the majority of seats in the Reichstag in 1932, they were still in a powerful position that they were able to use to manipulate the system a lot. I don't know what the appropriate legal course of events would have been had Hitler not seized power, but if they had a new presidential election, he would almost certainly have won anyway.

The answer to this question, in the sense of if Hitler gained power democratically, is no.

Germany was not a presidential system but a a parliamentary system (still is), so while the position of president was certainly important, the real importance lay in parliamentary elections. In those, the best outcome for the NSDAP was in the Reichstag elections of July 1932, where the NSDAP had the most mandates with 230 or about 37% of the vote. This put them on par with the KPD and the SPD, which combined gained 229 mandates or about 36% of the total vote (14.6 for the KPD, 21.6 for the SPD). This meant that Hitler could have formed a government but refused to do so because Hindenburg would not confirm him as chancellor.

In the November 1932 elections, the NSDAP fell to 33% compared to the 36% of the KPD and SPD combined. Here, a government involving the NSDAP was formed with Hitler as chancellor after Franz von Papen had reassured Hindenburg that he could keep him in check. In February 1933, the Reichstag fire happened and all sorts of emergency legislation with the aim of persecuting communists and social democrats was enacted since it didn't require the vote of parliament anymore. Even the passage of the Reichtag fire decree was undemocratic because the number of seats of the KPD were not counted towards the necessary members of parliament present to enact the law.

The elections of March 1933 were not free elections because of intimidation tactics by the Nazis and the fact that so many SPD and KPD members were imprisoned or otherwise stopped from voting that the total result can not be seen as representative. So, while in this election the Nazis had their best outcome yet with 43.9% of the vote, given the history surrounding this election and the fact that the Reichstag fire decree, which formed the basis for the Nazi takeover of power did not come to pass through democratic means, Hitler's government can not be called democratically legitimate.

As for Hitler's election platform, communism and the economy featured as big themes but not immigration. Immigration was rather irrelevant at the time, except maybe in the sense that emigration from Germany to somewhere else had become a problem.

As for the campaign's stance on Jews, while the subject did feature, especially in connection to communism and international capital, what was made were mostly vague threads of paying them back and so forth rather than any concrete program.