As someone who works in biomedical research and who has a prominent family history of cancer, maybe I can explain a few things about diet and cancer?
1. Yes, it has been shown that eating a certain way will lower (or increase) your likelihood of getting certain types of cancer. Eating too much, or eating not enough plants, have both been shown to substantially increase your risk of cancer (along with plenty of other diseases). This is not a controversial statement in science - scientists might not be sure about the exact degree that diet matters, but consensus has been reached that it does play a role.
2. No, it has not been shown that eating a certain way can cure or help treat cancer once you have it. This does not mean that diet definitely won't help someone with cancer - it just means we haven't proved one way or another. We don't know! This is definitely an area of active research and controversy in the scientific community right now. Current medical thinking is that patients should be free to try altering their diet (within reason) but that diet should not be used as a substitute for proven anti-cancer therapies (e.g. chemotherapy).
3. Chemotherapy is not "poison". It does make you feel sick, so people sometimes use "poison" as a short-hand to explain how chemotherapy works and feels, but it's an oversimplification of the truth. There are a lot of different ways that chemotherapies work, but usually they target rapidly-growing cells. Most cells in your body don't grow that fast, so they aren't affected at all by chemotherapy. Some cells do grow fast - for example, hair cells, immune cells, and cancer cells. Unfortunately, I've seen first-hand what cancer can do to a body, so believe me when I say that in most cases, the temporary terrible side effects of chemotherapy are better than the alternative.
If you want to learn more about diet and cancer, feel free to PM me. I can send you sources or explain what I know.