Wart-like dermal lumps & other feline skin abnormalities

Question
My 11 year old, indoor-outdoor, neutered male Maine Coon has a few curious lumps.

One is on the jawline. It's sort of like a human wart but there's no discoloration. The fur on and around it is normal. The size is a bit smaller than a pencil eraser and it's a firm lump.
There's an identical wart-like bump on his neck area.

My other cat is a 5 year old indoor-only female siamese/persian mix who gets recurring black dirty skin specks in patches on her chin (close to her mouth. No, it's not flea dirt, it's in the skin but can be scraped off. I believe it may be feline acne.
What is the best way to treat it at home?

She also small, crusty spots that appear on her chest and on her back near the base of the tail.
There is no hair loss, no itching, no infection, and they are painless.
I remove them but they just return.
She's short haired and I keep her well groomed.
Anytime she has taken a bath, I've only used warm water & a towel.
I don't use any products on her fur or skin, and it's not a flea issue. She doesn't take any medication.
What is this and how can I treat it?

Answer
Any time we see skin tumors on a cat, we are worried that they can be malignant, because so many of them turn out to be cancers.  For the cat with the chin acne and the crusts, that is usually the result of some type of allergy.  Some cats get a bacterial infection in the hair follicles around the chin and so antibiotics may help, but the majority of them will respond to either a steroid drug (DepoMedrol) or a cyclosporine (Atopica) drug.  Sometimes a simple antihistamine treatment with chlorpheniramine will help an allergic cat.