Which best describes people who have personality anxiety disorders characterized by the unreasonable need for a person to behave in a certain way to prevent a certain outcome

That sounds like people with Obsessive Compulsive Disorder (OCD).

That would be compulsion.

You did not show us the image of the burger, but i shall try to answer as best i can.  when purchasing food, always consider the ingredients as well as the person who prepared it. consider if they were hygienic people or not, in case the burger was infected with bacteria. no mortal should place an infected burger into their mouth.