How do I use page_callback or pageshow to display an existing article, view, page, block, or a slide show?
If you want your app's front page to show a node, then you can just set the front page to that node, in settings.js:

drupalgap.settings.front = 'node/12';


Under the hood DrupalGap already has a page_callback (and pageshow) that can load and render all core entity types. As you noticed with nodes, you simply linke to node/[nid] to view a node.

As for blocks, DrupalGap does not interface with blocks stored in Drupal, instead DrupalGap can create its own blocks for display in the app: http://docs.drupalgap.org/7/Blocks