If you are talking about normal "liver enzymes" then yes, they can be normal in a patient with cirrhosis. The reason for this is that as the liver becomes cirrhotic scar tissue replaces normal cells. It is the cells which release liver enzymes when the "die". The more cells dying the higher the liver enzymes. But, when a lot of cells have been replaced with scar tissue there are not enough "live" cells left to die and release enzymes. Thus the liver enzymes can be normal and sometimes even lower than normal.
People refer to liver enzymes as liver function tests but they really aren't. They generally indicate liver injury.
If you are cirrhotic I would expect that these tests will be outside of normal range: bilirubin, serum albumin, protein, prothrombin time (PTT or INR), platelet count. These tests give a better idea of how the liver is functioning.
Yes. Although the scarring from cirrhosis is permanent, it is possible for liver function levels to return to within normal range.