What is the ruling on using permanent dyes for the hair of the head, eyebrows, and eyelashes? And is this considered a change to God's creation?

It is permissible to dye hair and eyebrows with colors other than black, and to dye eyelashes with black, provided the substance is not harmful. If the dye is permanent and alters Allah's creation, then it is forbidden, falling under the category of altering Allah's creation, like tattooing, plucking eyebrows (namṣ), and teeth filing (tafluj). What is mentioned in the question is an even greater alteration of Allah's creation. However, if the alteration is not permanent and fades away, like henna and kohl, then there is no harm in it.