Is it obligatory for a young man who knows there is a problem with his heart – which doctors have stated does not affect marriage – to inform the girl's family about it before marriage?

It is not permissible to conceal from one who wishes to marry a defect that affects the marital relationship. Defects that are considered to affect the relationship are those that prevent sexual intercourse or are repulsive and contagious, such as leprosy and vitiligo. Some scholars, like Ibn Al-Qayyim, have broadened this, holding that any defect that repels one spouse from the other and prevents the marital objectives of affection and mercy necessitates the option to annul the marriage. What is mentioned in the question is not considered an affecting defect because it is neither contagious nor repulsive, nor does it prevent enjoyment. Therefore, there is no obligation to inform the suitor about it.