The giblets, if supplied (many aren't nowadays) will be inside the chickens cavity, best access is from the tail end.
Do not wash a raw chicken under a running tap, you will (potentially) splash salmonella etc around your sink area.
For egg freshness, erm, well you put egg into jug of water. It will either sink or float. Sadly I cannot remember if float is fresh or foul, sorry - try chicken keepers topic perhaps? I am a chicken keeper but eggs don't last long enough in our house to go off.