All foods can fit into a healthy diet, but too much can cause you not to fit into your clothes. Yes, they do contain cholesterol, but dietary cholesterol isn't necessarily converted to the blood cholesterol that narrows arteries and is linked to heart disease. Eggs are low in saturated fat, which is more solid at room temperature. Saturated fat is linked more closely with heart disease than dietary cholesterol. More research is in progress.
Egg whites are the leanest protein source available and contain no fat or cholesterol.
You can substitute two egg whites for each whole egg in most recipes. Since eggs bring to mind Salmonella food poisoning and all the misery it entails, they should be handled with care. Both the yolk or the white can contain Salmonella. Start with clean hands, utensils and work areas. Thoroughly clean anything that has been in contact with raw eggs.