Definition and explanation by Google:
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=47334
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Definition and explanation by Google:
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=47334
Those 6 sub links are called "Sitelinks, Site Links". They generally show up when there is a direct match in terms of company and/or content.
If you want sitelinks for your page, you should optimize the pages and brand your site. After doing so, and doing a search you should receive those site links.
No, from what I know there is no way to find out as this is given and done by Google.
SEOmoz gathers information from Analytics as well, so that will not help. But Analytics will give you an idea of what is going on.
Yes, you should create shorter excerpts. There should also be an option on WordPress to allow more than one blog post on the home page, you should increase this number, so each page is differentiated better than the home page and blog post.