There are two checkboxes for each data source: View and Log. You can log data without viewing it, but cannot view without logging. Data must be collected in order to be displayed.
Since each data source is collecting different types of information, only one data source may be viewed at a time. You may simultaneously log as many as you wish.
It is possible to continue logging data after closing the Trace Viewer. This allows you to collect traces over a period of time when you suspect that an intermittent problem may be occurring. You should note however that trace files can quickly become large. Leaving the Trace Viewer running on a permanent basis is strongly discouraged.