So to answer the second question first, the Nazis didn't see any difference between religious and secular Jews. Official Nazi policy defined Jews by ancestry, so a person could be a practicing Christian and still be classified as a Jew, and murdered for it, by Nazi Germany. Perhaps most famous among these is Edith Stein, who was born Jewish but converted to Catholicism and was a nun--she was killed because Nazi policies classified people as Jewish based on their parentage.

On the first, the answer is still no, but it's a bit more complicated. The Nazis never made it a major focus of their policy to restrict of forbid Jewish practice. As far as I'm aware, Jewish religious practice was never made illegal.

However, the Nazi's general persecutions did include religious practice. Kristalnacht included the destruction of most German synagogues. But, there was not a particular desire to destroy synagogues over other buildings--Jewish-owned stores were vandalized as well. There are also accounts of things like Nazis forcing Jews to spit on Torah scrolls, and the like, but these seem to have been attempts to humiliate Jews in a culturally-meaningful way, rather than motivated out of a contempt of Jewish practice. It's also worth mentioning that a lot of the Nazi's antisemitic propaganda was at least partially directed at Judaism, though objection to Judaism was not the brunt of their antisemitism.

So they did attempt to prevent Jews from practicing Judaism, but mostly because they tried to prevent Jews from doing much of anything. They were interested in the destruction of Jewry, not just Jewish practice. The Nazis killed religious and secular Jews without distinction.