I want to have a widget that can search a keyword in all fields in multiple layers. Can the current Search widget, query widget, and/or the enhanced Search widget do the task?
The quick answer is no there is not a widget currently available that can do what you are wanting. All the avialable widgets like the OTB Search widget, query widget, and custom widgets like the eSearch widget and selection widget all use the query task and what you are wanting would require the use of the Find Task.