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I would kindly disagree, if the article is on a major publication and an editor manually included it there, it has tremendous link value. The only time these articles don't have much value is when the major media sites add these articles through some automated process, like automatically adding press releases based on certain keywords in them. Google could easily detect the difference between the two.
it's against Googles TOS, it's not illegal. You can report them to Google and they probably won't act on it. If they keep doing this they'll find themselves a victim of penguin.
My advice is to just keep doing all you can to make your site great and keep it white hat. If they're spam link building it most likely will come back to bite them in the @$$.
Links from adult sites sound weird though because anyone link building can do better than that even if they are spamming - perhaps another one of your other competitors is trying to knock them out, you should keep a close look at your incoming link profile to make sure no one is trying to get you penalized, the higher you are in the serps the more people there are who want to knock you out of position.
Here is a great interview with Duane Forrester, a Sr. Product Manager with Bing’s Webmaster Program. In his interview, he has some very good tips on how to get great exposure in Bing.
http://www.stonetemple.com/search-algorithms-and-bing-webmaster-tools-with-duane-forrester/
I wouldn't drop these pages that are bringing in a majority of your traffic and try to promote your new product on these pages.
http://thmedicalcallcenter.com/ is not redirecting to http://www.thmedicalcallcenter.com/
http://www.thmedicalcallcenter.com/ is not redirecting to http://thmedicalcallcenter.com/
so they are seen as two separate sites. you need to redirect one to the other, most people redirect the non www to the www. In your case Google sees your site as www. You should 301 redirect the non www to the www and run the tool again
Latent Semantic Indexing
http://www.seobook.com/archives/000657.shtml
I think they definitely do that for spamming reasons, otherwise you could make a million pages with latin text and only put your keyword repeated in the content and get it ranked.
A real article speaking about a topic would generally have similar related words also included in the article.
yes you can definitely do that. the only problem is that "luxury towels uk" is not a real phrase like "web conferencing services" which fits into a sentence and has good search volume.
"web conferencing" and "conferencing services"
"luxury towels" might be but "towels uk" is probably pretty weak
So basically you would need to incude instances of the phrase in your content "Shop our store for a wide variety of luxury towels uk and see our quality" it doesn't read proper. I would rethink the keywords.
Also, yes include the singular as well as the plural and variations and synonyms. Put similar words on the page that Google knows are related to towels such as bath, beach, microfiber, cotton etc and you can rank for long tail searches as well.
Get the YOAST SEO plugin and it will canonical your site properly, noindex your tags pages and add rel prev/next tags to your paginated pages for you 
in addition to helping you with a lot of other SEO elements on your WP site.
I see your site as number two in the Google rankings for designer radiators, so not sure why you're seeing it in number 21. Try logging in as a different user.
Some suggestions: Get rid of all your nofollow tags on all the links - page sculpting does not work in that fashion anymore. Also, you maybe overlinking on the home page, thereby greatly reducing the page juice of the home page - the nofollow tags do not stop your page juice from being diluted.
Only Desiger Radiators should be in the H1 tag. I would not put the following in a H1 tag.
<h1>Welcome to the Radiator Gallery...h1>
Do you track rankings of individual keywords and can you share those results. You might need to wait until the next Panda/Penguin update before your site gets properly reindexed.
One day is not a long time but look at the code on the site if you suspect something is wrong.Check out your meta robots tag and make sure you're not noindexing or nofollowing. Check your robots.txt file to make sure you're not blocking.
Or you can run this http://www.xml-sitemaps.com/ sitemap generator and see if the are crawling your pages or bailing on the first page. If they are crawling your site Google most likely is unless you are specifically disallowing Googlebot which I doubt.
I would also recommend to go to the site configuration - crawler access page in Google Webmaster and test many of your sites URL's to ensure that robots can access them. Test every unique URL format on your site like the search results page, product pages, category pages, etc... I always use this tool whenever I make any change in the robots.txt
neither are good in my opinion, the first is impossible to remember and the second has a S in the middle. Keep digging IMO.
Does she have a business name, might be better to go the brand name route.
That could not be your issue. I would look elsewhere. If you provide the actual URL we could take a look at it and see what could be done to improve rankings for the product pages.
Shalom - Your blocking the images folder in your robots.txt file.
Example URL:
http://cdn.seomoz.org/q/help-with-getting-no-conversions
Canonical is a RELATIVE link, should be an absolute link pointing to main domain: http://www.seomoz.org/q/help-with-getting-no-conversions
<link href='[/q/help-with-getting-no-conversions](view-source:http://cdn.seomoz.org/q/help-with-getting-no-conversions)' rel='<a class="attribute-value">canonical</a>' />
13,400 pages indexed in Google under cdn subdomain
go to google > site:http://cdn.seomoz.org
I've never heard of this, i'd be surprised to hear it is true. You can use a standalone player like Flowplayer and host this videos yourself pretty easily.
I wouldn't do that because Google is not going to update your title tag every day like clockwork so if you're thinking the title tag will line up with the pricing on the page that won't happen - the daily price on your page will be one thing and the title tag will be a price from a few days ago. It could be construed as misleading because the user will see one price in the title tag, click on it and see a different price on the page.
Some of our sites are seeing this as well. I would venture to say that this is a fluke and not a leading indicator that the snippets are coming back.
I am just reiterating what many have expressed before on these forums.
1. A percentage of page juice is lost with 301 redirects and you may not have enough page rank to maintain the same ranking positions.
2. Sometimes it takes a few weeks for the engines to process the 301 redirects and you just need to sit tight.
3. Keep checking Bing and Google Webmasters for any error or SEO issues.