Both aren't you and are you can be used in the first sentence. You can't use aren't they in the first sentence because it says 'you' at the front. Both don't they and do they can be used in the second sentence. Both sentences have a similar meaning no matter which one you use in them.

You'll get slightly different meanings if you use "aren't you" instead of "are you" and "don't they" instead of "do they". So, you're going to live in New Zealand, are you? So they want to enter the competition, do they? You would ask these after hearing about the facts for the first time. There is an element of surprise and newness. I'm going to the land of Kiwi. So, you're going to live in New Zealand, are you? They're going to test their dancing skills. So they want to enter the competition, do they? But, these are different. You're going to live in New Zealand, aren't you? They want to enter the competition, don't they? The person asking the question already knows these facts. These types of questions are used in response to something that might contradict them. I'm taking a trip to Africa. You're going to live in New Zealand, aren't you? They are practicing really hard. They want to enter the competition, don't they? I hope that makes sense.

There is a slip of the pen. I meant to say Can I use "aren't YOU" and "don't they" in the two sentences?