1. I think this largely depends on what your race/ethnicity variable is actually measuring. SES could be a confounder in the relationship between race/ethnicity and environmental toxin exposure, where the race/ethnicity variable is really picking up geographic distribution and proximity to environmental pollutants. Here, SES could be a confounder because it would in part determine race-based location, and also determine proximity to environmental pollutants. In the relationship between race/ethnicity and nutrition, SES could be a mediator by that people of color are of lower SES which leads to poorer nutrition. Finally, SES could be an effect modifier in the relationship between race/ethnicity and CAD if people of color were more likely to have hypertension, but this effect was somewhat mitigated by being of higher socioeconomic status and being able to access preventive healthcare.
2. I would want to study the relationship between income and birth outcomes, and examining whether or not this relationship differs by race. This could be done with a prospective cohort study, ideally recruiting people before they are pregnant so you could capture prenatal care engagement. You could either include an interaction term between race and SES in the model or look at the association between SES and birth outcomes across difference races.