How to change the display of case listings to show and/or sort on case ID
For both pages you're talking about it's templates/CRM/Case/Form/Selector.tpl, but what's interesting is that I know case id used to be there. Browsing the code history it looks like it was removed around v4.5, but without investigating further I can't say why. But take a look at 4.4 for example to see how it used to be. It's not sortable there, but might get you started.
https://github.com/civicrm/civicrm-core/blob/4.4/templates/CRM/Case/Form/Selector.tpl