Is it true that a cat that comes to the house is not normal and possesses a spirit, and that one should stop feeding it? And can a Muslim jinn take the form of a cat that is not black? And how can one know if an animal is a creature and not a jinn?

There is no harm for your mother in feeding the cat, and she will be rewarded for it, according to the Hadith (definition): "In every wet liver (living being), there is a reward." Jinn can take different forms, but the statement that a cat is inhabited by jinn merely because it stays around the house is a baseless conjecture that should not be heeded. It is natural for a cat to stay close to whoever feeds it. We do not have knowledge of ways to distinguish jinn manifested as an animal from a real animal.