How to have a popup calendar in a date view exposed filter?
This can be done with the Better Exposed Filters module.

Enable the module, set it as the exposed form handler under Advanced -> Exposed form style, on the BEF settings page dialog set the filter display option to "jQuery UI Datepicker". Save everything and you should be good to go.

Note that changing from the default date format may require you to implement hook_better_exposed_filters_display_options_alter.