I don't have fresh eggs yet, but have a hint to help with the peeling. It seems that everyone in my neighborhood has problems peeling boiled eggs - I wonder if it has anything to do with the altitude - around 7400 feet or so. I never had any problems when I lived in Wisconsin.
After the eggs have finished cooking, drain the water off, then dump them from the pan to a bowl and back to the pan, shaking them around a bit in the process to crack the shells. Then fill the pan with cold water and let them cool down. Don't shake them too hard so that you are breaking the eggs open, you just want to crack the shells a bit.
I always go from pan to bowl because I usually fill the pan as full as I can when I boil eggs, then I don't have enough room in the pan after cooking to shake them around.
My peeled eggs aren't perfect, but they have been alot better since I started doing this.