aeiou - the greenish tinge is over-cooking the yolk - keep cooking it and it will turn black. Always check the dates on your eggs - so many times we just take them out of the carton and place in the egg try in the fridge and we forget just how old they are!
A perfect boiled egg has a fluffy yellow yolk.
Place your eggs in a single layer in your pot and cover with COLD water. Although I boil mine for about 8 minutes - depending on pan, amount of eggs, water, etc. others have had success by removing the eggs from the heat as soon as the water comes to a full boil and let the eggs sit in the water for 15 to 20 minutes. Once mine have boiled I immediately plunge into cold water to stop the cooking process (never had a greenish tinge to my yolks!)
I "roll" mine on the board after giving it the egg a light tap to crack the shell and I have no problems removing the shells.
To make sure your eggs are fresh, put raw egg in a glass of water. If it lays on the bottom, it's fresh. If it is on the bottom, but the small end is up, it's still fine. If it is floating in the middle, but not on top, it should be safe, but not very fresh. If it floats, throw it away, it's a rotten egg.
I hope this helps!
MM