You've got a problem here. Elementary uses the Pantheon desktop, which few people have and which doesn't seem to be documented. This is a classic example of the rule that beginners should start with a well-known distro and a well-known desktop environment! The fact that Elementary has no user forum and their website is down today doesn't inspire confidence.
The only pictures I could find were in this old review
http://www.dedoimedo.com/computers/pantheon-de.html
Does your menu look like the first or second screen-shot? The second menu style definitely has a pdf viewer shown.
The filing system is, of course, irrelevant. As far as the terminal goes, if you type in the name of an application it will run, wherever it's been put. In practice, things normally go in /usr/share.