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.
If you put the eggs in a jug/bowl of water you can tell if they are fresh. If they float dont eat them, if they sink to the bottom and stay there then they are fresh. Often they stay fresh well past the date stamp (at least a week)
Or you can crack one open, if the yolk has 'creases' around the edge then its old but still edible. If it stinks to high heaven then probably not such a good idea.
Most chickens dont have giblets with them, if they do it usually says on the packet that it comes with them. If it does have them I usually find them stuffed inside the inner cavity so you have to put your hand in and pull the bag out.
Actually, for the eggs, it's more a case of what angle they lay at. If it's very fresh the egg with lie horizontally at the bottom of the glass of water. By about a week old they tend to lie semi-horizontally, and when they are stale it floats in a vertical position, but can still be at the bottom of the glass or whatever.
If an egg has a hairline crack in it allowing more air in this might not work.
You can obvioule tell if an agg is actually 'off' the minute you crack it open though