When will one be able to
First, it is correct, yet not precise, it is supposed to be


  我什么时候能去中国？


Second and third, there is no question marker because "什么" already implied that this is a question, you would use "吗" when it is not obvious if the sentence is a question


  我能去中国吗？


Last, "能" corresponds to "able" in original expression. You use "会" for possibility, like


  他什么时候会去中国？


This means "when will he go to China?".