B and T Cells in the Immune System?

You are asking many questions. I'll just address phagocytosis. Unlike B and T cell activities, most phagocytosis is not particularly antigen-specific, rather it is part of the "innate" immune system. Generally, foreign antigens are recognized as foreign by "pattern recognition" molecules - often Toll-like receptors (TLRs). When TLRs are activated on phagocytic cells, they can stimulate these cells - mainly macrophages and neutrophils - to engulf foreign particles into vessicles called endosomes. These endosomes can then fuse with other vessicles called lysosomes. Lysosomes are filled with acid and enzymes that break things down - especially proteases. When an endosome fuses with a lysosome, it is called a phagolysosome. Most bacteria are killed in phagolysosomes. Some pathogenic bacteria survive by escaping from phagolysosomes or by preventing phagolysosome formation.