할 때 is just 'When Somebody do Something'. However, 하면 is 'cause and effect' Ex) 내가 공부할 때 비가 왔다. It was raining when I studied 내가 공부하면 좋은 결과를 얻을 수 있을 것이다. If I study I will get high score

Not clear enough. 하면 means 'If someone do something.' 내가 질문하면 너는 대답해 can be translated to : If I ask, you answer. There is no 할태. If you mean 할 때, It means 'When someone do something.' 내가 질문할 때 너는 대답해 can be translated to : When I ask, you answer. If you mean 할테 as a 할테다, It means 'Gonna do something.' 나는 질문할테다 can be translated to : I'll gonna ask. And for the last and the most important : I think this way of approaching is not that good to learn Korean. If I asked you about the difference between 'Do' and 'Did', you can say that it is present tense and past tense, but you can't say that the 'D' in both words have the same meaning, nor it has the meaning. And 'Di' of the 'Did' has no meaning too. But in Korean, '하-' has it's own meaning. '-면,' '-ㄹ 때,' '-테-,' '-다' has it's own meaning too. So, if you can understand each of five stems' meaning, you can understand 하다, 하면, 할 때, 할테면, 할테다. After that, you can learn ONE stem such as '-니.' And then, you can understand TWO OR MORE expression such as 하니, 할테니 or so. MOREOVER, if you learn '보다', you can naturally learn 보다, 보면, 볼 때, 볼테면, 볼테다, 보니, 볼테니. It's just my opinion, but I'm pretty sure that it is way more effective way to learn Korean. Hope your Korean-ability goes way forward. 화이팅!