Hey there! I'm happy to help!
Women were some of the principal advocates of prohibition, so they weren't likely to suddenly start consuming it once it was banned.
Migration didn't stop during prohibition because people who loved to drink alcohol could simply obtain it illegally. People usually came to the United States seeking a better life, and something like the alcohol ban would be something they could work around if they believed that immigrating would be much better for them.
Prohibition definitely did not hinder the growth of jazz music. In fact, it thrived during this time. This is because speakeasies, which were undercover night clubs that illegally served alcohol, frequently had jazz bands and performers. Since so many people wanted to consume alcohol, many people were exposed to this music and fell in love with it.
Since alcohol was illegal but so many people still wanted, it absolutely facilitated the growth of organized crime. Figures like Al Capone became some of the most infamous figures at the time because so many people were criminals for drinking alcohol that he was able to get out of going to court for more serious charges because the courts became so crowded. When so many Americans are criminals, it's easier for criminals to be more secretive. This is why prohibition failed and was eventually repealed with the 21st amendment.
Have a wonderful day and keep on learning! :D