https://www.sistani.org/english/qa/01130/
Can I keep a cat, hamster, and rabbit in my house?
Answer: There is no problem in it,
Note: The body and the salive of the cat, rabbit, and hamster is ritually pure (Tahir), yet its urine, feaces, and blood are Najis
Does cat hair affect ones prayers?
Answer: If there is a few cat hairs (one to three) on a person's body or cloth, his prayer is in order but if there are more than that, his prayer becomes void, as an obligatory precaution