Could an executive be given prison time for refusing to testify about what he knew about criminal activity that he was involved in at the company's facilities?

Yes. An officer is always liable for crimes committed by a corporation.

No$,$ under the Fifth Amendment privilege against self$-$incrimination.

No$,$ he cannot be punished for refusing to testify if his testimony could lead to civil charges against him.

Yes. He could be punished because refusing to testify is illegal.