Only B. However a little adjustment of your relative pronoun in C would work. "Why don't we do this the easy way in which you don't use that ... . Or, "I like the way (in which) you designed this." Know that there are other contexts where "the way that" works fine. "I don't like the way (that) you speak to me." The parentheses indicate that the words can be omitted. I can't think of a simple rule for picking. It seems to be very variable.

Charles is correct, but I thought I'd add to his answer. Think of the words after "way" as the answer to a question: "What is the easy way?" Since you're giving more information to the reader about what the easy way is, you need a pause in speech and a comma in writing. Therefore it becomes: "Why don't we do this the easy way, where you don't use that(,) and I don't make a mess?" I would say, though, that most native speakers would break this into two sentences: "Why don't we do this the easy way? You don't use that, and I don't make a mess." Anyway, keep up the good questions!

None of them are correct and natural, I think. But I'm afraid I can give you a suggestion since I don't really understand what you were talking about.

Only B sounds correct and natural.