Are the white oily secretions that emerge from the pores of oily skin considered impure, and do clothes become impure by them, or are they considered among the impurities that are overlooked due to their small size and difficulty in controlling them, and is prayer valid with their presence?

The substance in question is excused due to hardship, and there is no need to wash it from the garment. The prayer is valid despite its presence. The proof for this is that Al-Kharashi, the Maliki scholar, mentioned that traces of boils, scabies, and what results from them, such as blood, pus, serous fluid, and water flowing from a burn blister, are excused if they affect the garment or body, due to the difficulty of guarding against them if they flow on their own. Similarly, Mansour Al-Jamal, the Shafi'i scholar, mentioned that things like boils and wounds are excused, even if they are numerous, due to the widespread nature of the affliction.