What is the difference between just saying "I didn't wanna do this" and "I didn't wanna have to do this"? Is he saying it to emphasize that he really didn't want to do this? Is it common to say like this?
Yes, you are right, the addition of "have" in "I didn't wanna have to do this" serves as emphasis of the fact that he really doesn't want to do something. In addition, the word "have" here also implies that it was not a choice for him to make, but he was obligated or forced to do it. So "I didn't wanna do this" means that you don't want to do something but you are choosing to do it, while "I didn't wanna have to do this" means you don't want to do something and it isn't your choice to do it. It is fairly common to use "have" in this case when you want to imply that something wasn't your choice. Here's an example of this: Ex: I didn't want to cook chicken but I had chicken to use up anyways. Ex: I didn't want to have to eat eggs but that's all I had left in the fridge. In the first sentence, you don't want to cook chicken but you choose to do it anyways because it is convenient. In the second sentence, you don't want to eat eggs but you don't have a choice because that's the only thing you have to eat. Hope that helps!