Is it permissible to read the Quran and listen to it at the same time to ensure correct pronunciation? And is it permissible to read the Quran without wudu'? And is one who tries to memorize parts of the Quran without reading the rest considered to be abandoning the Quran?

There is no objection to learning the rules of recitation from a cassette tape or other means, provided the reciter is proficient. There is also no objection to reciting along with it for practice. Similarly, one who gradually memorizes the Qur’an is not considered to have abandoned it.