Not sure if I understand the immune tesponse

I'll do my best to answer but I'll mainly be referring to my textbooks which may contradict what you've said so take my answer with a pinch of salt...

From what I understand, when memory cells recognise an antigen they stimulate the rapid production and secretion of antibodies by the B-plasma cells. These B-plasma cells are produced as B cells rapidly mutliply by mitosis and differentiate into plasma cells in a process called clonal selection. Therefore while I'm not sure how memory cells affect T cell production, they certainly lead to the production of B cells.

To this end, B cells are needed because B-plasma cells can secrete large amounts of antibodies. By the time that the T-helper and cytotoxic cells are doing their jobs responding to the infection, the pathogen may have multiplied to a huge population. The T-Cytotoxic cells cannot kill the pathogens as fast as they are replicating so B cells secrete antibodies to rapidly kill large quantities of pathogens to end the infection.
Hope this helped!

1) I know that that T memory cells remain in circulation. However, am I right in saying that once exposed to the same antigen the T memory cells develop into T helper and cytotoxic T cells?

2) Why are B cells needed? Why can’t the pathogens be destroyed through the cellular response in the first place?

1) I know that that T memory cells remain in circulation. However, am I right in saying that once exposed to the same antigen the T memory cells develop into T helper and cytotoxic T cells?

2) Why are B cells needed? Why can’t the pathogens be destroyed through the cellular response in the first place?

Also, B cells and T cells target pathogens in different locations. B cells (or more precisely, antibodies) produce antibody which can bind to free antigens/pathogens in the circulation. Cytotoxic T cells, on the other hand, do not kill free pathogens, they only kill intracellular pathogens - that is, pathogens that have invaded other cells.

The simple answer is: T cells alone might not be enough. Antibodies help. A lot.