If there is no rooster near, then the eggs can't be fertile; unless you have another specie close to a chicken? Once the yolk is broken it is nearly impossible to ascertain fertility. With the yolk intact, there wold be a small white bullseye on the yolk if fertile.
I don't think so. Did you see anything that looked like the fertile egg fertil photo. Maybe if you see anything again, post a pic of an egg that isn't broken. I would be fascinating if it was fertil though!
All eggs have a version of that. It has nothing to do with fertility. It is part of the egg formation process. I don't recall at the moment what it is called. Fertility is shown by the white dot somewhere on the yolk. If it is a plain white dot: not fertile. If the dot looks like a "bullseye" white ring around the dot: fertile. Search the forums for fertile eggs and you will find pictures.
Domestic fowl can be crossed, and produce fertile offspring, with silver pheasants, red junglefowl and green junglefowl. They have also produced hybrids with peafowl, chachalacas, capercaillie, grouse, quail, curassows, pheasants and guans.
I guess my previous post did not get posted. No rooster-no fertile eggs unless you happen to have one of the above mentioned species; also guineas.