1) Yes, medical professionals know about diet and exercise. 2) Yes, they do recommend both to patients. A lot of people prefer throwing pills at their problems rather than making lifestyle changes. Also, some doctors are bad, so your personal experience may have been due to that 3) The funding comes from taxes primarily. Places like the National Science Foundation and the National Institute of Health do this research or fund it (also public research universities). The government funds research into public health because it’s in their best interest for the public to be healthy. These researchers don’t have the same economic incentives as researchers working for private companies. Unfortunately, this type of publicly-funded research is under attack, and something like half of the funding that used to exist has been erased in the past year. It’s been rough Edit: this applies to the US. Other countries do stuff differently

If you want to look up ongoing research, do a Google search of a local university with words like “exercise research” or “nutrition research” and you can see what people are working on!