SEO - explain google page rank, alexa rank, and others

Hi,

My web site has finally reached a point where I can begin to concentrate on marketing it, rather than codeing it.  Although I've read how alexa explains their ranking system, and I understand google's page rank is supposed to be an indication of popularity, but something is just not clicking in my understanding of their meanings.  I have a google pr of 5 but very little traffic to my web site.  And I've seen sites with hugh traffic numbers compared to mine with a much lower google pr.  And the same with alexa, I've seen dead pages with much higher rank than mine.  

-1-  Please explain page rank as it applies to google, alexa, and if there is any other ranking system, or links to tools, web sites, etc that tells realistically what other sites do in comparison.  

-2-  What can I do to increase my search engine presence?  I paid an SEO company a large amount, but after 6 months they still had no results to show for it.  I'm not in the top 1,000 sites for any keyword in my category of batteries.  I have lots of text for search engines to capture, and almost every line of text on my home page is from a reverse search engine top results, so something else is seriously wrong with my site.

-3-  Finally, the first box of 9 links in the top of the left margin is totally unnecessary to the function of the web site.  They just add unnecessary clutter.  I'd like to remove them, but they each bring up an additional page with a google rank of 3 (if "www" is added to their url).  Will removing them cause a drop in my page rank and/or a drop in my already low search engine presence?

Thank you for your help.  I will split points.  Please give me some indication of your expertise in seo when giving your opinions to point 3 above.  I've had answers for point 3 from one extreme to another.

Thank you.

Steve
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