Your question is not a simple "which one is correct and why" because each one is problemmatic, whether in syntax or in logic. Assuming that you're talking about manipulating time-space continuum: #1 The "Is it mutable..." structure is a question (when you have verb + subject), so the absence of a question mark here makes it incorrect. #2 and #3 are the same sentence, with just the "it is" contracted to "it's". The "could" is problemmatic in both cases. If you change the (time-space) continuum, you directly affect time, so the appropriate verb here is "would" because there is a definite consequence. It is not just a possibility, which is what is implied in a "could" statement.

Either 2 or 3 are correct, depending on the tone you want. 1. This is structured like a question. 2. This is the most formal. 3. This is more informal. Are you writing science-fiction by any chance?