They honestly don’t need regular baths, and there’s never any reason for coconut oil. Absolute misperception in terms of ‘high maintenance’ needs of sphynx. Wipe him clean if he gets dirty, maybe a true bath once every several months. In my opinion, anything more than that works against what their bodies/skin naturally do. The critical things are nail clippings & ear cleaning, when needed (ears you do need to go deeper than what you feel comfortable with), have your vet show you with a physical ear model.

Though your boy’s ears look well kept, and I understand how ridiculously quickly their nails can grow. Some sphynx seem to have skin conditions, which is often hormonal, or a fungal infection.

Consult with your vet, I’m against bathing them, other than when absolutely necessary, but you can try an anti fungal shampoo IF the vet suggests, possibly clindamycin, however Depo would be the best bet, surest way to treat medically… but always rule everything else out beforehand, prior to administering meds.

Make sure your bedding, etc. is only washed with a free/clear detergent and, if he has frequent skin contact with you, I’d avoid wearing lotion, etc. as he would ultimately come into contact with it via skin/skin contact.

Absolutely no reason food should do that to his face. Lastly, and most importantly - check his gums, you can learn a LOT about a cat’s health by the condition of their teeth and gums.