Can fatty live be cured?

Absolutely. The most common cause is lack of exercise, followed by alcohol overindulgence. Other causes (diabetes, hepatitis c, several inborn errors of metabolism) have specific treatments. I'm glad this was discovered, as it can become serious, but as long as cirrhosis hasn't supervened (which is a miserable way to die), you can probably take charge of your own recovery and enjoy doing it.
Yes & No. If it is related to alcohol consumption it may be reversible if there is no established liver scarring. Life style and dietary modification are the main stays for non- alcoholic fatty liver disease.