This question is asking us what we wanted to be as a child. Remember to conjugate the たい portion of the verb for tense. We will say that we wanted to be a doctor as a child.

子供の時、医者になりたかったです。
（子どもの時、医者になりたかったです。）

This question is asking us if we have ever had a dog or a cat. We will say that yes, we have had both a dog and a cat. Remember to use the particle と instead of the particle や when referring to an exhaustive list.

はい、猫と犬を飼ったことがあります。
（はい、ねこといぬをかったことがあります。）

This question is asking us what we want to be now. We will say that we now want to be a Japanese teacher because we love studying the language. Remember to put the reason before the conclusion and join them with the proper verb forms.

今は日本語を勉強するのが大好きだから、日本語の先生になりたいです。
（今は日本語をべんきょうするのが大すきだから、日本語の先生になりたいです。）