Should I write my Listening answers in capital letters?

The answer is that punctuation is not marked in the IELTS Listening or Reading tests, so it doesn't matter whether you use capital letters (upper case) or lower case letters to write your answers.

However, if you are taking IELTS On Paper, it is advised that you write all of your answers on the Listening answer sheet in capital letters (upper case). This is because the answer sheet will be scanned, and then read and scored by computer and capital letters are usually clearer and easier to read accurately than lower case.

If you are taking IELTS On Computer, it does not matter. Use capital letters, lower case, or the normal mix.