Is there a module that provides a drop-down select box on anode/add form to select a page template to be applied to a node?
This can be done using Display Suite Extras - View Mode Switcher (and very nicely it works too) but only works for nodes at present. Basically you enable view mode switcher in the extras settings page, add the view mode switcher field to each of the displays you wish it to be available on (all of which are customisable template files through display suites layout template system). Now when you visit the node you will get a list of the display modes (which can be labelled as you like) to switch between inline using ajax.