Does small cyst of morgagni in female go away on it own?if so how long does it take?does essiac tea help dissolve it?does this cyst cause infertility?

Usually not: Unless it bursts open it will not go away on its own. And even if it does burst the cyst is still there. It really should not affect your ability to get pregnant.

'No' to above: It's an embryologic remnant, it's been there since before you were born. They do not go away and don't cause fertility issues unless they become large. Large ones may twist or rupture and need surgical removal. Tea does not affect them in any way.