Diet and chemo. There is no "special immune building" diet recommended for patients undergoing chemotherapy. In general a balanced diet with enough proteins and fruits/ vegetables is preferable. Chemo can suppress appetite but it is very important to maintain your weight while going through these therapies.
Healthy diet. In general probably foods high in good healthy nutrients like lots of veggies, berries and fruit. However, you may want to ask your oncologist to refer you to a dietician to evaluate your current diet and make further recommendations. Food with high levels of antioxidants may help also. Probably a good balance of lean protein if you are losing weight will help also.
Does cancer weaken the immune system or does the medication for the cancer (chemotherapy) weaken the immune system?
Cancer and immunity. Interesting question. Cancer usually either fools or overwhelms the immune system as the latter usually keeps cancer cells in check. Medications for cancer vary, some kill the good and the bad and wipe out the immune system with the cancer cells and the new biologics are targeted therapy that only kill cancer cells. Science is progressing, stay tuned..