Just like any other book, to memorize the Quran you need to keep on reading the verses until you can remember them without looking on the Quran. However, this will take time since you need to take time on one chapter to understand it before moving to the next.
Don't. That won't teach you a thing useful for 21st century. Just a waste of your precious time to learn the prejudices and nonsense of people who lived over 1000 years ago. And I would say that about any religious book, it's just a BOOK.