They are all correct. In Russian you usually should use full constructions when mentioning something for the first time and then you can omit words pretty much because we already know what you are talking about. We use greetings so often that we like to omit as much as we can. - Как у тебя/твои дела идут? - how things are moving? (kind of a question if they walk the good way or the bad way). Here you can see all words used in there places - Спасибо, хорошо. - things in my life take the good way - дела идут хорошо. But in colloquial speech we tend to make it shorter and omit some unnecessary words: - Как дела? - You don't have to use "тебя" as it is clear that you are asking the person in front of you. The absence of a word is some kind of a "self" marker as well. In English you say "I met my sister" in Russian we say "я встретил сестру" (we don't have to say "my" because in Russian the absence of the word is meaningful, it means that you speak about object related to subject). Also we omit the verb, because we know that nothing else can be used there but that very verb. And that is how you get "как дела?". So here you use this: Как дела? - Хорошо, а у тебя? The second your example is related to the full phrase "как ты поживаешь?" which becomes shorter "как поживаешь?" or "как ты?". The full answer to that is "я поживаю хорошо, спасибо" but we never say it, we stick to "хорошо" only and then you may add "а ты? Как твои дела? - Хорошо, а у тебя? - as you talk about the things. Как ты? - Хорошо, а ты? - as you talk about a person.

There is one more important note. In Russian people usually just start conversation without these "How are you"s things. Sometimes when friends haven't seen each other for a while they can ask this "Как дела" but it's not the same as English "How are you". Actually it doesn't matter what you answer. You just have to say something like "Норм" or "Да нормально", "Не жалуюсь", etc. And in my opinion it's too polite to answer with "А как у тебя дела?" because the question of your friend wasn't about "дела" - it was just ot start chatting. So you can answer "Нормально" and just continue wherever you want.

The fullest version is probably "- Как у тебя идут дела? - У меня дела идут хорошо, а как идут дела у тебя?" Also sometimes the questions takes form of "Как (идут) ТВОИ дела?" but you still answer that with "У меня..." and not "мои дела.."

«Как дела?», «Как жизнь?» и «Чем занимаешься?» are often asked out of courtesy or to keep the ball rolling . Possible answers: 1) when everything is fine: «Хорошо, а как у тебя?». So you just switch conversation to your partner and want him to tell you about himself. «Отлично!», "Лучше всех!" This is a kind of a positive answer which assumes that the further discussion also will be developed in a positive way «Нормально» It is a neutral answer. The following discussion might concern any subject 2) when everything is not well «Не очень» After that answer a person who answered expects that you ask him "Why?" and he/she gives you details. «Неважно….»And the a partner start to explain "why" without any question from your side. «Плохо, но не хочу об этом».In that case a partner tries to switch discussion to another subject and also he/she could say "Лучше о себе расскажи"

Dear Shane, You can respond "У меня дела хорошо/Дела хорошо/Все хорошо, а как у тебя дела/а у тебя/а как ты? These combinations of 2 parts of the sentences are full answer to " Как дела/Как у тебя дела?"