My cat has worms. HELP!?

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I own 2 cats and I recently discovered that my longhair Siamese has worms. She's 3 years old and my other cat is 7. They have been living together for approximately 3 months. I first suspected the worms when I noticed stringy rice-like things attached to the hair near her anus. Then I saw one crawling on her feces like a Brown Mountain. I have never dealt with worms before and I have a few questions. I don't expect You to answer them all but please answer at least 1. Thanks. 1) I saw no evidence that my other cat caught it. How do I know if she has it? 2) Can I or other members of my household be at risk for the parasite? 3) How can I determine what kind of worm I'm dealing with? 4) Should I put both of my cats on medication? Thanks and I need some fast help.