I have two SEO optimised pages in my website targeting different keywords

www.example.com                 <-- main selling page (Pocket Guitar | Guitar Instruments)
www.example.com/index/       <-- 2nd selling page (Guitar Australia | Guitar Perth)

Q: At first my website "www.example.com" is ranking on google first page. Suddenly it disappears and the link "www.example.com/index/" appears instead.

No matter what i search, "Pocket Guitar | Guitar Instruments | Guitar Australia | Guitar Perth", the link www.example.com/index/ appears on the front page instead of www.example.com.

What is happening to my main domain? Should i be worried?

Q: Does a link in a facebook post count as a backlink?

Q: is it a 'do follow' or 'no follow' link?

Q: twitter uses short links, so when someone links to me, do i get the points/juice from the backlink?

I notice that many sites have sub headings appearing below their google results.

http://i.imgur.com/A5JxMKD.png
See image for example.

Q: what are these called? and how do we get them?

A5JxMKD.png

Q: Does a link in a facebook post count as a backlink?

Q: is it a 'do follow' or 'no follow' link?

Q: twitter uses short links, so when someone links to me, do i get the points/juice from the backlink?

I notice that many sites have sub headings appearing below their google results.

http://i.imgur.com/A5JxMKD.png
See image for example.

Q: what are these called? and how do we get them?

A5JxMKD.png