Thank you, kareem and vera. Because of you, I understood the differences among the phrases. I'd like to use them very naturally in the future. Thank you again.

"I don't know" is used when you clearly don't have the answer to something or information. "I am not sure" is used when you have some information but you are uncertain of it. However, they can be used interchangeably. Example: Q- what ingredients do you need to bake this cake? A- I don't know (because I haven't checked the recipe) Q- It seems the recipe requires chocolate; which one do you think we should use, milk or dark chocolate? A- I am not sure. "I don't understand/It doesn't make sense" are used when you have information but you cannot interpret it in a coherent way. Example: the use and application of the particle が in Japanese doesn't make sense to me; I don't understand how to use it. :P　 These are very, *very* simplistic examples, of course. Drop me a line if you have questions!

- Did this guy kill his father ? 1- " I don't know " means you have absolutely no idea. 2- " I'm not sure " means you think he did it but not 100% sure. 3- " it doesn't make sense " means you also don't know but you think he didn't do it because he may be a good guy so it doesn't make any sense to you that he might commit such a murder