Can Fatty Liver cause hair loss?

Yes, fatty liver can cause hair thinning and it may reflect some other condition going on that could precipitate genetic balding if you have the genes for balding.  For most men (98%), thinning and hair loss is genetic.  Here is an article reflecting the general safety of minoxidil with regard to liver toxicity: https://www.ncbi.nlm.nih.gov/books/NBK548394/