How long does it take to recover from alcoholic hepatitis? Can this disease cause HE?

Acute or chronic? Acute alcoholic hepatitis will cause a rise in your liver enzymes and the damage will be transient but continued alcohol consumption may lead to chronic hepatitis with cirhossis and other sequelae including hepatic encephalopathy. If you know alcohol is a problem for you or a loved one, you should get help before it becomes irreversible.
Difficult to say. Without understanding how severe the case of alcohol hepatitis, as in the most severe cases(rare) sometimes liver transplantation is necessary. Hepatic encephalopathy can be seen in more severe cases of alcoholic hepatitis.