Why is it that a dog will spend a lot of time looking for a perfect corner to hide a bone, then give itself away by running to it, growling, showing it's teeth, when you let it know that you are looking for the bone?

It's pack mentality. They establish pecking order and even play that way. Sparky will do that and hold off the two bigs dogs even though in reality he would be hamburger.

Why do they turn three times then lie down?

Muffin is not very smart. She does not know a bone from an ear of corn. I gave her the tip of the small end ear of corn I had for lunch. She cleaned the cob and tried to get me to chase her. I made a couple of moves her way and gave up. I later came in and told her that I was going to get her bone. She ran to the hidden cob and started growling at me.

She does know when we are getting ready to go hunting. She won't leave my side.