Can liver problems cause pulmonary fibrosis?

No. Cirrhosis is associated with two other lung disorders which can cause similar symptoms to pulmonary fibrosis. These are called hepatopulmonary syndrome and portopulmonary hypertension. These only occur if cirrhosis is present. If it goes on long enough without treatment, portopulmonary hypertension can cause permanent injury to the lung.
Depends. There are many systemic diseases which involve both the lung and the liver. Hence there are instances where pulmonary fibrosis is associated with liver abnormality. In general, isolated liver abnormality does not cause pulmonary fibrosis.