The first one (more right is "у меня есть этА кошка") means that you have this definite cat, and the second sounds like someone asked you "What is that you have?" and you're answering that this is a cat here with you. And if you just want to say that you have a cat you might say "У меня есть кошка". (And "У меня есть кот" if the cat is male.)
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Has difficulty understanding even short answers in this language.
Can ask simple questions and can understand simple answers.
Can ask all types of general questions and can understand longer answers.
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