If you see blood like that JDS3 posted your deer will be "bedded down" permanently a very short distance away. In addition to the color difference, as you can see, there is a definite spray pattern from a lung hit.
Heart and liver hits will leave splashes of blood as a rule, but they need to have an exit wound low enough on the body for it to escape as a rule. I have seen heart/liver hits with little to no blood trail, but a body cavity filled with blood. Not much fun, but usually they won't be far away.
Muscle blood can be dark or bright red depending on whether an artery is involved. These can mean a long day or night.
Yes, a deer may lie down after a hit. If not pushed, assuming a mortal hit, they will stay right there and bleed out. I'm not sure about them bedding down with the arrow still in them. Most of them either break it off or the arrow slides out as they run, or they just tip over in sight with the arrow still in them. If they run very far, I doubt that the arrow will remain intact.