For the search, you could emulate the functionality that the SD.Feeder.TechnicianIncidentForms workflow uses. For assignments you can do it one of two ways. You can either assign it using the Assignments section in the Dialog Workflow component. To be honest, I can't remember if it's the Group ID or the group name that you would populate in this field. Otherwise you could do it using the AddTaskAssigment component. The mapping definition for the component is:
AssignmentDate: Process Mapping using the Get Current Date component.
ReferenceID: Mapped to the group's ID
ReferenceName: Mapped to the group's name
ReferenceType: Set to Group
TaskAssignmentID: Process Mapping using the Create Globally Unique Value component
TaskID: Set to workflowTaskId variable (This is usually set in the Dialog Workflow component)
With the last example, I've put this component in the Start Process model under the Dialog Workflow component's Event Configuration tab. This way I could use the workflowTaskId variable.
Hope this helps.