depends on what you are trying to express

Yeh.you are right.

非常正确。。。But you might want to consider it a little bit redundant in some situations. and there's a more concise way you may use when talking that is "我不管” provided that you were arguing for simply one reason, or “不顾一切" when writing. If you are saying a reason or a state when doing something, you might want to add 了 to make it 我什么都不管了。 anyway我什么都不管了is correct grammatically, and sounds normal