What matters is that you hold a class 1 medical certificate. The certificate is a temporary qualification of your assesed state of health commensurate with your age and any notified restrictions. Provided you hold such a certificate I can't imagine that many companies are going to ask you anything else on this subject. Obviously if there is anything particularly relevant in your own case it may be incumbent upon you to disclose it to a potential employer, however I doubt your parents health would necessarily fall into that category.
From what you have written it seems you have been advised that your family medical profile has suggested you may be at higher than average risk of heart disease. Advice to eat healthily, monitor your blood pressure and likewise your cholestorol is all good advice. In fact it would be good advice for most of the population. Sensibly following such advice will not "put a nail in your coffin" quite the opposite in fact, it ought to take a nail out of it !