what extent does the criminal law impose liability for omissions? Is the law in this area in a satisfactory?

Answer 1

I personally feel that it is more than satisfactory. If you want more on omissions and how they are applied in respect to criminal liability, look at the Model Penal Code. It is quite different from omissions under Tort. To see more about civil liability for omissions look at the Restatement of Torts (Second).

Answer 2

You know you ain't gonna get people here to write your essay for you.

Omissions are all over the place in criminal law anyway, think of health & safety.