The five types of leukocytes are: neutrophils, lymphocytes, monocytes, eosinophils, and basophils. Three of these (neutrophils, eosinophils, and basophils) contain granules, tiny sacs containing enzymes which can lyse microorganisms. The other two leukocytes (lymphocytes and monocytes) do not contain these granules.

T cells, especially CD4+ follicular helper T cells, are absolutely critical and necessary for the induction and maintenance of germinal centers.  

IgE plays a critical role in induction and promotion of type I hypersensitivity (allergy, asthma, etc.) normally through engagement of Fc receptors on the surface of basophils and mast cells, which primes them to produce large quantities of granules and chemical mediators (including histamines and cytokines).

B cells play numerous integral roles in the immune response against foreign pathogens (viruses, bacteria, and fungi), including forming transient microenvironments called germinal centers, where they produce long-lived plasma cells that are high affinity for specific antigen and memory B cells. They also serve as antigen-presenting cells and producers of cytokines and chemokines; However, B cells are not able to produce extracellular traps, which primarily are composed of DNA and work to trap pathogens. Neutrophils produce extracellular traps.

The following helper T cells are paired with the following cytokines:

Th1 - IFN-gamma

Th2 - IL-4

Th9 - IL-9

Th17 - IL-17

Tfh - IL-21

Autoimmunity arises when one's immune system is unable to recognize its own MHC proteins, which could potentially lead to aberrant activation of the immune response. Furthermore, autoreactive immune cells that are normally induced to undergo apoptosis may be able to escape these tolerance mechanisms and induce tissue damage.

Natural killer (NK) cells are prominent members of the initial innate immune response against foreign pathogens. They play numerous integral roles in the innate response including cytotoxic killing, cytokine production, and antibody-mediated cell cytotoxicity. 

Cells of myeloid lineage include dendritic cells, monocytes, macrophages, neutrophils, basophils, and eosinophils, while cells of lymphoid lineage include NK cells, B cells and T cells.

Naive B cells (and most other immune cell subtypes) need more than one signal to become activated. They normally need B cell receptor signaling (signal 1), costimulation by other receptors (signal 2), and cytokines/chemokines (signal 3). This system is necessary in order to prevent aberrant activation of lymphocytes (safeguard against autoimmunity).  

In regards to the other statements, there are numerous autoreactive B cells at any given time due to the stochastic nature of VDJ recombination and germinal center reactions. Therefore, tolerance mechanisms and checkpoints are incredibly important to keep these cells in check; central and peripheral tolerance are equally important. Self-nuclear reactive B cells and T cells are both necessary and critical in autoimmune pathogenesis. Female sex hormones are definitely believed to contribute greatly to autoimmune disease pathogenesis (e.g. estrogen). Over 75% of autoimmune patients are women.

Peripheral tolerance is the correct term for the tolerance checkpoint mechanisms that are instituted in the secondary lymphoid organs such as spleen and lymph nodes. B cells with BCR specificities that are low affinity or reactive against self-nuclear antigen will be purged from the repertoire.