Customizing CP Entries section template First, which template does the actionGetElements use to generate a response?

Second, how can I customize the template for a single entry section?
First, there isn't a single specific template that ElementIndexController's actionGetElements uses to return data.

It implements IElementType's getIndexHtml method which BaseElementType provides a default implementation of, but any ElementType (Entry, User, Asset, custom plugin ElementType, etc.) is free to implement that method with their own logic.

Second, it sounds like you want to hack core files in the craft/app folder, which I definitely wouldn't recommend.

You might be able to make the modifications you're looking for with something like the CP CSS and CP JS plugins.