Why no ma?

那是你的妻子吗？would be a better translation; Is that your wife?

You use "是不是" to ask a question, when you already assume an answer.

So for example: 那是不是你的妻子？; Isn't that your wife? 你是不是要茶? ; Don't you want tea? ect..

Why this app doesn't provide the pinyin system? It would be useful for vocabulary and pronunciation...

Is 的 mandatory here? I put 那是不是你妻子

为什么“那个是你的妻子吗”不对吗？

Yes! So much for using Ma when asking a yes or no question.

和 那是你的妻子？

Is there a way to let duolingo know that 的 is not used with close family/spouse?

This is not a good translation. Should be asking : isn't that your wife? Since it's got a negative in the wording of the question

What about "这个是你的妻子吗？“ Does that work?

I know the point of that lecture is probably to also get the 是不是 thing across, but wouldn't 这是你的妻子吗 also be a correct solution?