Regarding diet and lifestyle changes --
Well, this is just my opinion, but here goes...
I think it is incredibly easy to be fooled by randomness. A good illustration from finance is the "stock picking newsletter" scam.
That scam goes like this.
Pick 1000 people and send them a "free stock pick of the month." The scam part involves sending each one of the 1000 people a DIFFERENT stock pick.
For illustration, assume half the stocks go up after 1 month and half go down. At this point, there are 500 people that got a "winning" stock pick from me the first month. Take that group of 500 and send them another "free stock pick of the month." Again, send all 500 a different stock pick. After another month goes by, do the same thing to the 250 that have now got two "winning" picks in a row.
Now, after 3 months, there will on average be 125 people that have, for three straight months(!), gotten a stock pick that has turned out to be a good pick. To this 125 people you send them a special offer to subscribe to your newsletter for the introductory price of $10,000 or some such nonsense.
Anyway, the idea is that the people receiving the stock picks only see the picks made for them (not the picks made to other people). By shear random chance, a good fraction of them will see a sequence of good picks and will be inclined to buy the newsletter. That is the stock picking newsletter scam.
In medicine, the same issue arrises. It is not at all a scam, but rather the issue is that each patient mostly only sees what is happening to them. For example, suppose 10 cancer patients add a "no sugar" rule to their diet. Perhaps one of those 10 has a very good response to treatment. It would be very natural for that patient to attribute some of the good response to the "no sugar" regime.
Similarly, 10 patients might decide to add lots of exercise (or olive oil, or anything really), and again perhaps 1 has a strong positive response. This person is likely to suspect that exercise played a role in their response.
Now it could just be that one in 10 patients have a strong response by shear chance alone (even if they don't make any major lifestyle changes).
How to combat randomness? In my opinion, the best way we have to guard against getting fooled by randomness is the clinical trial.
While it could be that certain diet changes have an effect on cancer outcomes, it may not. Just as the people receiving the newsletters could be fooled by randomness, so can cancer patients.
For me, the take away is to try and be healthy, but don't do things that seriously negatively impact quality of life unless there is good supportive evidence.
I also believe that participating in a clinical trial plays an incredibly important part in trying to improve patient treatments. Without clinical trials, randomness can slow down treatment innovation to a crawl.
Again just my take on things.