Why is it we get zero points for answering some questions, but we do for others? Does it have to be new questions we answer, not old ones?

Yahoo Answers lets people answer questions now, that already have a Best Answer chosen. If you add an answer to a question that is already resolved you don't get any points for it.

Because points aren't earned for questions that have BA's chosen or for answering your own.

You do not get points for n answering your own question

you do not get points for answering questions that already have BA awarded.

Also sometimes it is a glitch or bug that says you got 0 points when in fact you did. look at your points history