How long would it take for a reversible dilated cardiomyopathy to correct by itself?

Cardiomyopathy. That is variable so no time can be put on that also not all cardiomyopathies are reversible.
With treatment... From my experience a few weeks to a year with appropriate measures such as right medicines, restoring blood flow as in bypass surgery, surgical correction of heart valve problems, controlling blood pressure, correction of rapid heart beat or abstinence from alcohol.
That varies. It depends on exactly what you mean. With medication, there can be improvement quickly. Most of the time there is not a cure, but the symptoms can be controlled. In certain unusual cases, the problem can completely resolve so that the problem does "correct itself." that usually occurs over a period of many weeks or months. It is a gradual process. Cardiomyopathy related to pregnancy can resolve.