The correct answers are Not only did the chef burn the soufflé, but he also insulted my tie, Rarely have I experienced such profound disappointment in a dessert, and On no account should the soup be served at room temperature.

When a sentence begins with a negative or restrictive adverbial (like not only, rarely, little, under no circumstances, or on no account), we must invert the subject and the auxiliary verb.

"Under no circumstances you should eat" is incorrect because it lacks inversion (it should be should you eat).

"Little the waiter knew" is incorrect because it lacks the auxiliary "did" (it should be Little did the waiter know).