Is it permissible for a young male student to receive lessons in Quran and Tajwid from a woman who is a stranger to him and is 47 years old, and would this mixing (ikhtilat) invalidate his work in memorizing the Holy Quran?

The questioner should seek a man to teach him the Qur'an. If this is difficult and he only finds his father's cousin's daughter, then there is no harm in that, provided that Islamic guidelines are adhered to, such as not being in seclusion (khalwa (definition)), adhering to the legal hijab (definition), and not speaking in a soft, enticing manner. This is because the questioner is the one who will recite to her. As for the belief that good deeds are nullified due to mixing, this is not correct.