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You don't need to worry about some sort of duplicate content penalty for using the same image/filename all over your site.  This is common practice, for example, Amazon uses the same logo image file on every page of their site.

We have had good luck with the SEO package from PRWeb, although it is pretty pricey.

Sounds like a bot or scraper to me.  That's strange because usually bots/scrapers don't execute javascript which is needed to show up in Google Analytics.  What analytics package do you use?

Make sure to use a 301-redirect and you shouldn't have any problems.  If those domain have any existing links, then the 301 will also pass most of the link juice to your primary domain.

It doesn't hurt to have them, but I don't think there is any real benefit to them anymore for the search engines.  They should be able to find all of your pages by following the regular links on your site.  That being said, I still have them on my sites.

Our press releases have been picked up by many online sources and we got some do-followed links from them.

Hard to say, I doubt you would be penalized for only incoming links if your site is clean. But you may always have that history. You could add the site to webmaster tools and submit a reinclusion request explaining the situation. They maybe be able to "wipe the slate clean" for you.

here's a great post from SEOmoz about it: http://www.seomoz.org/blog/complete-guide-to-rel-canonical-how-to-and-why-not

I think the advice in that article is still relevant today.  Create a footer link to the "website credits" page, and give yourself a link from THAT page.

I think business.com directory links are valuable.  Check the mozRank of the page that your link would be on and make your decision based on that.

Anyway to dig in to see what search engine those referring keywords come from?  Like craven22 said, it might be an image search.

Your understanding is correct.  You want to 301 them (or use canonical, but 301 is better) and NOT use a domain alias.

Since the content on the whitepaper would be significantly different from the content on your lead form, I wouldn't do it.  That doesn't mean it wouldn't work, it might, but I wouldn't do it.

Put it in the /blog subdirectory and your main domain authority will pass to it.  Make sure you link to the blog from your main site.  We have the same issue as you, and at first hosted on blog.domain.com but later moved to domain.com/blog based on advice from many people at SEOmoz.

To make sure the value is passed around, be sure to liberally link to and from the blog to other areas of your site.

Yes, you can say CGI parameters = URL parameters.  I don't think many people refer to them as CGI parameters anymore though.

To answer your question, yes, as long as you have rel canonical set up correctly, then the URL parameters won't hurt your indexing.

For example, if you have your rel canonical set to http://mysite.com/japan.html

Then, only that page will be indexed, even if there are various parameters such as

http://mysite.com/japan.html?source=something&whateva=somethingelse

Just MAKE SURE to setup rel canonical correctly because it can be bad if you don't.  Check out Dr. Pete's post about this: http://www.seomoz.org/blog/catastrophic-canonicalization

Are you using "home care blog" and "in home care agency locator" as the target phrases on the other pages that you are linking to? For example, are you targeting "home care" on the discussed page, and the others phrase on other pages?

If so, I'd say to ignore the link cannibalization warning.

I think you're going to run into trouble.  If you insist on keeping them separate, you need to be good at covering your tracks.  Otherwise, you could do it the white hat way and 301 all those domains to your main domain.  But, you would lose the built up branding of those other businesses.

I seriously doubt you would be penalized, but Google (the algorithm) is going to know you are just duplicating product titles and not give it any weight and ignore it.  Why muck up the page for your human customers?