How long and how many years or months can a cyst or a tumor that is benign turn into malignant?

It is unpredictable: The true cysts are benign and therefore do not change into cancer. But cysts can have a focus of cancer which is initially hidden but tends to grow over a period of few months, so monitoring of its size at 3-6 month intervals is advised to be sure that it is not growing in size. Increase in size may be a signal that it should be removed to be sure that there is no cancer inside the cyst.

Forget about it: Most cysts will never turn into anything, same for benign tumors. Your doctor will advise you if you need further tests.

Whoa: The vast majority of cysts / tumors / tumors that are also cysts that are benign will never turn malignant. If there is a reasonable chance that you have a mass that is or may be cancer, and it can be removed, it needs to happen, now. A few masses (notably a fibroid uterus) can be watched; rapid growth of one mass would prompt removal which is fairly safe.