First, about "nolle prosequi" (Latin term for "will no further prosecute") is a term commonly used in criminal law to denote that the prosecuting attorney will no longer prosecute the case or will withdraw his charges in a criminal proceeding. In a civil proceeding, the plaintiff files a "motion to withdraw" his complaint or pleading, or the records already in the court. In most cases, the plaintiff, instead of filing anything, simply "fails to appear" before the judge,and the case will then be dismissed by the court.

Second, about the term "compromise and settlement" or more commonly "settlement" for 和解, Black's Law Dictionary defines it to mean "an agreement arrived at, either in court or out of court, for settling a dispute...." The Chinese term 自行和解 means actually "settlement arrvied at out of court between the parties voluntarily and willingly, although the court may play the role as a mediator under Chapter 8 of the Civil Procedure Law. If you feel you have to translate the expression 自行, perhaps you can say "voluntary compromise and settlement."