Answer:
I don't live within a house nor do I live without. Most will use me when they come in and again when they go out.
I can run but not walk. Wherever I go thought follows close behind.
I turn around once. What is out will not get in. I turn around again. What is in will not get out.
You bury me when Iβm alive and dig me up when Iβm dead. What am I?
I go up and down at the same time. Up towards to sky and down towards the ground
I flow from the Homerβs mouth when he sees doughnuts.