Mirena coil contains hormones which may change body metabolism. but this change in metabolism is not too prominent to cause any serious adverse effects.
Liver cyst can be any thing from polycystic liver disease
, hydatid cyst
etc I cant comment on it unless further evaluation.
Fatty liver is nothing serious, it usually occurs with increase in cholesterol
level in blood. Fatty liver may be alcoholic or non-alcoholic.
We need your lipid profile
to relate the problem to cholesterol.