Reading through your letter, it sounds like there are two issues going on here. First is the blood countsproblems: the low white count, and the high red count. Low white blood cells are usually caused by cancers, severe bacterial or viral infections, or immune disorders (like HIV/AIDS or lupus). A high red cells count is caused by a disorder called polycythemia vera. This is a genetic condition that causes the bone marrow to produce too many blood cells, so it is not caused by a liver problem. This disorder sometimes causes high white counts too, so I am not sure why your father's count is low.
The second issue is that you don't know what is going on with your father's health. This may be because your father is still being "worked up", which means they are still exploring what is causing his problems. You did mention he was having problems with vomiting, so the referral to the liver specialist may be for that. Or perhaps, when doing tests, the doctors found an abnormality with his liver. What I would recommend would be to have a "family meeting" with you, your father, and the doctors, so that you can talk about what the doctors know so far. Perhaps that will help you know where your father stands with his health issues.