Office Actions are basically the response to your patent application. On average, you can expect to receive an office action around 18+ months after you file your patent application. In the Office Action, they will either ask you to change the claims, specification, drawings, etc. And they may also ask you to present arguments why your invention deserves a patent in light of the prior art.

Patent Prosecution just refers to the back-and-forth between the USPTO and the Patent Attorney. The examiner reconciles the drafts of the patent application with the Patent Attorney.

Patent Prosecution does not refer to litigation or Infringement. And it also has nothing to do with criminal law either. Instead, Patent Prosecution merely refers to the negotiation and response to office actions received by the United States Patent & Trademark Office (USPTO).