How to retrieve Worklist item using the .GetWorklistItems(filter) of Management API?

I don't think there's a direct way to query it, but if you know the Destination user, it can be quite simple. Sample code below:

WFM.WorkflowManagementServer wfmServer = new SourceCode.Workflow.Management.WorkflowManagementServer();

            int iProcInstID = 10,

                iActInstID = 11;

            try

            {

                wfmServer.CreateConnection();

                wfmServer.Connection.Open("Integrated=True;IsPrimaryLogin=True;Authenticate=True;EncryptedPassword=False;Host=blackpearl;Port=5555");

                WFM.Criteria.WorklistCriteriaFilter oFilter = new SourceCode.Workflow.Management.Criteria.WorklistCriteriaFilter();

                oFilter.AddRegularFilter(WFM.WorklistFields.Destination, SourceCode.Workflow.Management.Criteria.Comparison.Equals, "K2:DenallixAnthony");

                WFM.WorklistItems oItems = wfmServer.GetWorklistItems(oFilter);

                foreach (WFM.WorklistItem oItem in oItems)

                {

                    if (oItem.ProcInstID == iProcInstID &&

                        oItem.ActInstDestID == iActInstID)

                        wfmServer.RedirectWorklistItem("UserA", "UserB",

                            oItem.ProcInstID, oItem.ActInstDestID,

                            oItem.ID);

                }

            }

            finally

            {

                if (wfmServer.Connection != null && wfmServer.Connection.IsConnected)

                    wfmServer.Connection.Close();

            }

Yes, have a look at the WorkflowManagementServer object in the Help File, it has methods to Stop and Delete instances.