I've applied an intership to prepare for grad school, but the acceptance result won't be sent before the deadline. Should I mention it in my SOP? If everything goes smoothly, then before going to the grad school in fall next year, I will have an three-month long internship. The problem is, the admittance result will come after the deadline of the PhD application. What I can only say for now is that I have applied to that internship.  

Should I mention it in my SOP and CV? Since I'm switching the field, getting that internship will be a strong proof that I'm capable on this field. And if I should, how to mention it?
Even asserting about the plan of the internship within the SoP would be valuable. Because it certainly depicts your plans for the future, as a succession of the intentions, could which be continued with pursuing the target graduate program, purposefully.
You better to stress on the expected outcomes of that internship within the SoP, would which be along the recent research projects in the target department in order to increase the applied coherency.

On the otherhand, CV is supposed to cover one's preceding accomplishments (and even might consist of current and unfinalized affairs, just like a submitted), but mentioning the uncertain points about the future (may which never happen!) does not fit, reasonably, within its scope.