"It doesn't matter" often means "don't worry, it is not a problem" or "don't say sorry." "I don't mind" often means "you have my permission" (e.g. "may I borrow your pen?" "Sure, I don't mind"). "I don't care" is more negative; it implies something is not important to you, or that you don't respect it (e.g. "your sister is really angry at you." "So what? I don't care.")

1. 'It doesn't matter' means 'It's not important'. You often use this when someone says 'Sorry', meaning 'It's OK/ No problem/ Don't worry about it'. For example, your friend forgets to give back a book that she has borrowed, and you say 'It doesn't matter. I've got another copy at home.' 'I don't mind' means 'That's OK with me'. For example, if your friend offers you apple or orange juice, and you say 'I don't mind', it means that you'd be happy to have either drink. 'I don't care' means 'That doesn't interest me'. This can be quite a rude reply, depending on the situation. You probably wouldn't say this in the two situations above with your friend, because the answer would seem a bit rude. But if someone told you some news about your ex-boyfriend, maybe in order to upset you, you might say 'I don't care! It's over. He can do what he wants.' 2. Of the three questions, the first is ungrammatical. We would never say that. 'What's happening?' is a neutral question. You can say that in any situation. 'What's the matter?' is what you might say when you can see that something is wrong.

For your first question: "It doesn't matter," "I don't care," and "I don't mind" are all correct. They all mean pretty much the same thing, but I'd say that "I don't care" can be a little bit more general. For your second question: "What is happening?" is the only one that can be considered a greeting. "What is the matter?" is also grammatically correct, but it's not a greeting. You would say it to a crying person, to find out why they are sad.