First, determine the freshness of your eggs before boiling them by putting them in a bowl of water, they sink to the bottom if they are fresh, they tend to raise if they are a few days old. The shell is porous, air gets in and store at one end, that makes them want to float, if you get a depression at one end, it is the indication that your eggs are a few weeks old.
To cook them you may boil them for 12 minutes or bring the water to a full boil, turn off the heat and let them stand for 30 minutes at least. Using salt or vinegar is to coagulate the white if the shell cracks.
Place your eggs under running cold water to stop the cooking and to avoid the dark ring around the yolk. Sulfur and albumen meet at this level as they cook, stopping the cooking by running cold water will prevent this formation.
I used to teach Home Ecs and raise laying hens, simply hope that this ''lecture''will answer some of your concerns,