Is the job of Phagocytosis simply to eat microorganisms ? Are there anymicroorganisms that Phagocytosis can't eat ?

Yes, phagocytes are part of your immune system and
immunologic response. They help to protect us from disease. Phagocytes are a type of
leukocyte as is a neutrophil. Phagocytes search out and engulf and destroy foreign
invaders in the blood like bacteria, viruses, and
fungi.

Yes, there are many microorganisms that the
phagocytes can't engulf and destroy. Cancer cells are a good example. Most types of
cancer are transmitted through the lymphatic system not the bloodstream.  Certain
leukemia's are susceptible to phagocytosis but the number of immature leukocytes seen in
leukemia is so great that the phagocytes can not destroy enough to make any appreciable
change in the patients condition.