The black residue on the chin and possibly around the mouth is called Persian Dirty Face, I have found nothing that does anything better than washing/cleaning it daily and if it's bad twice daily. It's really kitty acne and can be mild to severe. You might try using porcelain or stainless steel feeding dishes, anything but plastic. Our case is mild and the keeping it clean does the trick. However if it's severe, perhaps more can be done. Take a look @ this site.

http://www.fabcats.org/owners/skin/acne.html

I have persians and two of them have the rust coloured eye discharge, it's mild and I use something I bought online called Angel Eyes, it's a cleaner and then you treat the fur around the stains. It works fabulously, and lasts a long time.

http://www.angelseyesonline.com/

The tail thing sounds like stud tail. It's a greasy, sometimes scabby residue. Not all cats get it..I suspect the severity of your cats stud tail (scabbing after cleaning) is high. You can wash him with a degreasing shampoo, or also recommended is Dawn dishwashing detergent, they use this to clean oil off of birds and other animals after oil spills. It may take a few treatments, once you have the scabbing off you need to keep it clean, and might even need an ointment/antibiotic cream to heal it, then regular bathing constantly after that. I would imagine that's painful. If he's white when you get that under control you can buy cat shampoo's (or use a dog shampoo) that is specifically for white ones.

This site tells you how to clean it up and gives recommendations for keeping it under control. I hope your cat is neutered, non neutered cats have a higher instance of stud tail.

http://www.purrinlot.com/cat-stud-tail.htm

You could also get a good groomer to clean him up the first time, and then you do the maintenance.

I hope this helps, and good luck.

I'd also recommend a new vet.