Below solution covers most of raised ideas for widget usage.
Below philosophy is both the most flexible and really quick and comfortable for user I can image. It uses existing powerful filters/views/(and templates - that developers work on) for quickest selection.
It gives both minimum clicks/touches and maximum flexibility = ultimate usability.

1. VIEW CHANGE:
   1a. User in widget settings checks [v] views he wants for the widget
   1b. Widget has button "change view" that displays list of selected views to switch between quickly.
   1c. If only two view are activated for the widget, view switches between the two ones right away (without list displaying).

2. [+] ADD TASK (the same philosophy):
   2a. User in widget settings checks [v] templates for new tasks he wants for the widget.
   2b. Widget has button [+] ("new task") that displays list of selected templates for quick selection.
   2c. If only one template is activated for a widget, it starts right away (without list displaying).

3. OPEN ULTIMATE TASK LIST APP (the same philosophy):
   3a. User in widget settings checks [v] views/folders he wants for the widget.
   3b. Widget has button "open ultimate task list app" that displays list of selected views/folders for quick selection.
   3c. If only one folder/view is activated for a widget, it runs right away (without list displaying).

(Due to widget many settings, "change widget settings" button seems must be available too).