Is it advisable to enroll in the “Hufaz al-Wahyyayn Association” course for memorizing the Holy Quran in 15 days, and to what extent are its claims true, and does it have any side effects on the mind?

If you seek knowledge, be sure to acquire it from those whose competence you are certain of. Ibn Sirin said: "Indeed, this knowledge is religion, so be careful from whom you take your religion." As for the website you are asking about, we do not know those who run it nor their teaching methodology. We advise against rushing in memorization and learning. It was narrated from Az-Zuhri that he said: "Whoever seeks knowledge all at once will lose it all at once; knowledge is acquired over days and nights."