To address each of your questions -
1) Why does the bilirubin levels reduce as long as she is in the hospital? whereas once she went home within 6 days things got worse? Is it related to the plasma that she takes?
The bilirubin is likely getting better in the hospital because intensive treatment in the hospital is more effective. The plasma, itself, is probably only a single component of that care, and while it is important to prevent bleeding complications, it usually would not significantly affect the function of the liver in metabolizing bilirubin. Other aspects of care, such as albumin infusions, diuretics to control ascites, etc., would have a greater effect on liver functioning.
2) Is there any possibility for the liver to cure itself at this stage with proper medicines and diet? (I read about some cases who had cirrhosis stage 3-4 from alcoholic and it reversed back to stage 2)
There are some cases of cirrhosis that will improve significantly when the underlying cause is eliminated or corrected, such as the example that you note. In her case, if the underlying cause was the fatty infiltration of the liver and she has no further evidence of fatty infiltration, then her underlying cause has improved, but she has not had similar improvement in liver function, so it would be unlikely that she will cure itself or significantly improve. Adjustment of her medicine regimen may get better control of symptoms, but the cirrhosis, itself, will not likely improve.
3) Can the liver get worse even with medicines and proper diet?
The liver can get worse, even with optimal medical care and lifestyle management. Although there are some cases of cirrhosis that improve with elimination or correction of the underlying cause, as discussed above, most cases of cirrhosis that have progressed to this severity are progressive.
4) How can someone with fatty liver turn to reach this point (liver failure)?
Someone with fatty infiltration of the liver can develop chronic inflammation of the liver. Any cause of chronic inflammation of the liver can develop scarring, which is the hallmark of cirrhosis. As the scarring gets worse, the normal architecture of the liver is lost, so that the blood does not percolate through the liver normally, so that impurities that would normally be removed from the blood, such as bilirubin and ammonia, will instead become elevated.
5) How can you tell if someone is fit for a liver transplant surgery?
The primary determinant of whether someone is fit for a liver transplant is their overall health. A liver transplant is a very major surgery. Obviously, anyone being considered for a liver transplant is unhealthy from the perspective of their liver, but there also needs to be consideration of the health of other organs, particularly their heart, lungs, and kidneys, to judge whether they are a candidate for transplant.
If I can provide any further information, please let me know.