For viewing the report on a screen this is pretty easy. You accomplish this by passing parameters from a perspective page exactly as you suggest. The default report starts with two parameters, StartDate and EndDate. You have to create objects in the params section of the report viewer component with the same names as your report parameters (as shown in the picture below). Bind these to any date source (there are several components that would work depending on your graphical preference), and everything should work. One note of caution, when you first create the objects in props.params, it will look like your report is broken because the parameter values have the wrong type. Put valid sample values in and everything should work like it's supposed to.
For the export the process is similar. In system.report.executeAndDistribute you can pass parameters as strings. Get the values from your date picker components (or create the dates based on some logic you prefer) and pass them as parameters in the function call.