After they are done boiling, immediately in ice water and let them coolI also crack them before putting them in ice water.
I have a process for boiled eggs. The older the egg the better. If I can (or remember) I take the eggs out of the fridge a few hours before making them (room temp eggs seems to be easier to make)....
You can shell a hard boiled egg by grabbing both ends and turning them opposite ways. Be Gentle.
maybe in vinegar but it will take a very long time
Roll the egg on a hard surface until the shell is completely cracked and crazed. Peel off shell under running water.