The paper below describes the isolation from various tissues (not liver, but you could try similar methods?)
Activation can be assessed by flow cytometry (activation/degranulation markers: CD203c & CD63 for example), if you know how to obtain single cell suspensions. Otherwise, people use mast cell stabilizers, and analyse whether the secretion of cytokines or other mast cell mediators such as histamine are affected.
am not sure about Livermast cells, but mast cells from the peritoneal cavity can be isolated by Ficoll or layering the tissue homogenate on 35% BSA layering method. mast cell can be confirmed by staining with toluidine blue, as they show metachromasia.
Connective tissue type of mast cells can be stained with toluidine blue whereas mucosal types could be stained at acidic pH by alcian blue. Liver mast cellsmight be connective tissue type. Confirm it first then try type of stain.