The Like button is in the main unzip file in the modules directory. However, you only need to install that if you're want to use the Like button in a module. If you want to use the Content Plugin to automatically add the like or comment widget to articles, you don't need to install the Like or Comments module.
On the page you linked too, I actually see the Like button and comment box at the top of the article. At the bottom of the article, I see another Like button which is coming from K2 itself. I'd recommend disabling that button and configuring JFBConnect (in the Social area) to show the button at top and bottom, if that's what you want.
Finally, in the Configuration -> Misc tab, there is a setting in the "Experimental" area like "Strip tags from head". Please enable that as it will fix the issue of showing {JFBCLike ...} at the top of your page.
Let me know if you're still having issues, but again, from what I see, you've got things going; maybe just need to change some of your configuration settings to change the positions of things more.
Thanks,
Alex