How long does it take a salivary cyst to get off naturally (amount if years)?

Mucocele. If you are referring to a mucous retention cyst of a minor salivary gland within your mouth, these are persistent, can have periods of quiescence, then re-inflame. They do not "self resolve". Patients usually accidentally bite the mucocele and further traumatize it and have secondary focal fibrous hyperplasia. Best to have it evaluated, properly identified, and if indeed mucocele - excised.
Hmmm. Where, size, how long present? Sorry, but we can't give you a good answer to that one over the internet. Ask the doctor who diagnosed it for the best answer to your question. Small ones may break on their own or be easily punctured by your dentist and never return. Some reoccur and many have to be surgically removed, especially the larger ones.