What is the ruling on asking Allah for the improvement of hair and skin, for success in matters of this world and the hereafter, for deliverance from Satan, and for the enlightenment of the mind by Him? Is this permissible?

It is permissible to supplicate for every matter that is permissible and ordinarily possible, even in small matters like a sandal strap, as mentioned in the hadith. What is forbidden is transgressing in supplication, such as asking for unlawful things, or things that are ordinarily impossible, or what is not befitting for the supplicant, or what Allah does not do, such as asking for immortality or infallibility, as explained by Ibn Taymiyyah.