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Try installing the plugin I suggested. You changed the permalink structure that was followed previously, so you will want to make sure they get redirected properly. The plugin I mentioned will do just that. There is also the off chance that you need to empty the cache of your website via your cache plugin, or server side.

Wordpress and other software either comes designed for SEO, or has plug-ins which offer SEO abilities. They work by automating some tasks for you. For example, they can automatically canonicalize pages or use friendly URLs. Any SEO options you set up must be thoroughly inspected. While they do make things easier, I would never treat it as a "set it and forget it". Many people get away with that approach, but others do not.

It will direct the link juice from the redirected URL to your page, as long as you use a 301 (permanently moved) redirect. This will pass 90-99% of link juice from the linking URL. To squeeze out everything you can get (pardon the pun) ideally you want a direct link, but a redirect will pass most of your juice along in the case you would have to get people to change hundreds / thousands of links.

by going with either of these (/xxx/pr-123.php vs /xxx/www-pr-123.php) you are signaling to the search engines that "xxx" is the common factor and each page within that "virtual" folder would then be seen as a sub-set.  So the question then is whether "www-pr-123.php" or "pr-123.php" is more appropriate for SEO purposes. I'd say that it all depends on the importance of the "www" portion.  If "www" is in fact a relevant word/phrase, either from a general search value or from a brand identity value, then it's best practices to include them in the URL.  If they're neither valued for search by people who are not familiar with your specific products, or alternately, not important to people looking up your products who already know them, you can leave them out. Another take on this would be - what's the chances someone would search for the products by part number without the www portion?  And what's the chances of someone searching for the products by the "www" portion only? While it's not necessarily critical to include every single aspect of a part's known naming convention in the URL (if you have optimized page Titles, h1, content, image names, etc), I'm guessing you want to cover the bases in how people search based on different situations, so in that case, don't leave them out. As far as the concept of having too many URLs saturated with any aspect of category, product name or whatever, there's no need to be concerned with that if they're valid products grouped properly.  It's more important to provide unique quality content on every single page.  And if you're talking about many very similar products, that itself should be your biggest worry. Just having the same descriptions repeated over and over page to page, with just a single word or part number being the difference is what would be the problem.  Coming up with 100 or 150 or 200 words that are uniquely written for every product - now that's the bigger goal and far outweighs the URL repetition. Then there's the fact that if you have all those repeated URLs, you're actually telling search engines "we've got a lot of relevant products for that topical focus".  But only if you get those unique descriptions done right.

As was said, a high quality link from a non-relevant site still brings some value with it. If you want to play it just a bit safer, you might try presenting those links as some "partner" sites that provide your visitors with "special rates" or "discounts", when they are visiting you. It might not hold any water in an algorithmic analysis, but in a human review, I suspect it would help.

The site I have seen the most for WP templates is: http://themeforest.net/ I have no personal experience with the site so I cannot comment further. There are plenty of sites which offer designs if you are unhappy with that site. They seem expensive to me, but they have a ton of designs and several look exceptionally nice.

If all your dealers are running your copy on their sites, verbatim, that could be a piece of your problem... certainly worth looking at. It's not uncommon for an affiliate to out rank their principal even though the principal had the original content up for a year or more prior. Another thing worth keeping in the back of your mind, as you chase this down - sometimes we don't drop in the SERPs because we dropped, but rather because someone else ROSE.