Is it permissible for a man to learn Quranic recitations from a woman who is not a محرم (a close relative whom he is forbidden to marry), and is he obligated to joke with her if she is very old?

Learning the recitations requires significant effort and a long time, and it may lead to unlawful seclusion (khalwa). Therefore, a man should receive knowledge from men as long as they are available. If that is not possible, then there is no harm in learning from a woman, provided that Islamic regulations are observed, such as avoiding seclusion, and not speaking in a soft or alluring manner. Indeed, the Companions used to receive knowledge from female Companions and the Mothers of the Believers. As for joking with a non-mahram woman, it is impermissible, and it is not permissible to speak with her except out of necessity, limiting the conversation to the extent of that necessity, and without speaking in a soft or alluring manner, even if she is elderly.