Is it permissible for someone who has memorized only a small portion of the Quran to lead people in prayer, using an earpiece to listen to the Quran and recite it?

If you are reading to those present (i.e., from the mushaf), then there is no harm in you leading them in prayer. Otherwise, do not lead them, and let the one who is most knowledgeable of the Quran lead them, for the Prophet, peace and blessings be upon him, said: "The one who is most knowledgeable of the Book of Allah should lead the people in prayer." Do not wear earphones during the Imamah, as this can be a distraction, and some jurists consider the prayer invalid with such a recitation aid. Recite what is easy for you from the Quran from what you have memorized.