Not usually. It's a different animal – you need to create a separate version for ePub.
Master page elements, for example are not exported and you have to ensure that all text has paragraph and character styles applied, that all images are anchored and so on.
Producing simple ePubs from InDesign is not intuitive, but reasonably straight forward once you understand how they work (ePub3 is based on HTML5 and CSS3). There are two types of ePub – fixed layout and reflowable text ePubs (the Kindle uses a propriety version called a mobi file and you can convert your ePub to a mobi format).
I would recommend that you have a look at Anne-Marie Concepcion's tutorials on Lynda.com. For example: http://www.lynda.com/EPUB-tutorials/InDesign-CC-EPUB-Fundamentals/143324-2.html
I believe you can get a free week's trial.
Of course you can also ask specific questions on the InDesign ePub forum.
Moved to InDesign EPUB forum.
In answer to your second question, you select Digital Publishing as the intent. And it's definitely best to have the latest version on InDesign which is at the moment, CC 2014.1