The reason she is doing this is her rear, belly itch. This can be due to fleas, worms, diet , or the glands around her rectum being full. The hair clumping on her back again can mean that she is scratching this area. If the problem is fleas of course you may be able to take care of this with an over the counter product specifically labeled for cats. If she has other problems like allergies a skin infection diarrhea or impacted glands she will need to see the vet.
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If you live in Las Vegas, I guess fleas are not a problem. I'm jealous.
It is hard to say what she is rubbing into the carpet. It depends on what is making her itch. If the itching itself is not a problem, than You could wait and discuss the hair clumps with the vet at her next appointment for shots. (One less trip to the vet). Do watch for sores forming under the hair clump.
The TV commercial is trying to get the consumer to think the puppy is using the carpet as its toilet paper. If every time your cat or dog scooted you had the carpet cleaned. Your carpet would ware out in 2-3 years.
Also if the milk is not causing diarrhea than it is OK for her. Not all cats can drink milk.
I hope I have covered all of your question . If not let me know.