What is the ruling on going to a شيخ (sheikh) who heals with the Quran, recites over women, and is secluded with each one individually, and perhaps the woman stays in his house for a few days?

It is forbidden for a man to be in seclusion with a non-mahram woman, even if it is for Ruqyah, because the Prophet (peace and blessings be upon him) said: "No man is alone with a woman but the third of them is Satan." A woman staying in a house of a man who is a non-mahram to her for several nights and days is even more forbidden and dangerous, as it leads to evil and corruption. Therefore, whoever has done this must repent sincerely and not return to it.