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Many times when people say , my competitor has a spammy link profile, it turns out that among all the worthless links are a few really good ones.

If you see they are doing anything wrong report them to google, https://support.google.com/webmasters/answer/35265?hl=en

I did a crawl of your site using the Bing API and found many external links, but none to domex-uk.co.uk, I think this is a google error.

you do have a huge amount of external links, you are giving away a lot of link juice.

Having 2 or more domains will not help at all, it does not work link that. you would have to 301 redirect them to a single domain and that single domain is the only one that will help.

You could raise suspicion, but some sites go viral and build links naturally very quickly.

what I would suggest is that if you are building links quickly, they are probably crappy links. If you can get a link easily its probably worthless.

I don't believe there is a such a thing as google sandbox.

Spot on, unless your site is trying to spam results with DC, you don't have a problem,

And yes it would help google understand what you are doing.

google will find them unless you have hidden them behind no-index, but the number of internal links is not important, what is important is your linking structure.

http://thatsit.com.au/seo/tutorials/a-simple-explanation-of-pagerank

I would not no-index them, as links pointing to no-indexed pages waste link juice. I don't think you have a problem. The duplicate or thin content pages may not rank well, but they will not have a negative affect on your home page.

http://www.searchenginejournal.com/matt-cutts-explains-duplicate-content-affects-rankings/82327/

As long as your link text is relevant to the pages you should be fine.

But footer links are discounted buy search engines. and mostly missed by users. If you want those pages to rank I would be looking at putting the links further up the page.

Also linking to as many pages from the homepage as possible is a good thing, here is a good read about internal linking

http://thatsit.com.au/seo/tutorials/a-simple-explanation-of-pagerank

You can 301 any page to anywhere, that not a problem, but before you waste any time, only 301 the pages that have external links, there is no value in 301'ing pages unless they do.

You are spot on, all you are doing to hiding and showing, if you can see it with fetch as googlebot you have no problems.

I differ in thinking here on one point.

I believe that links pointing to the same page have the same decay as any other link. That page rank flows out of them just the same, obviously it goes to the same page but some of it is lost every time.

What I do and looks much better is use javascript to scroll to that spot,

$('html, body').animate({ scrollTop: $("#mytarget").offset().top - 70 }, 'slow');

This will scroll to your anchor, the offset lets you position things nice.Even if I am wrong, the scrolling animation looks and feels much better

I can see it fixed your problem, but its a ugly fix, you mean need to use parameters in the future, you may already be using them but unaware.

If the site is returning 200's then that is where the problem lies, you need to find out why.

I can see any other fix, removing the urls is only a temp fix, you must make them return 404's

That means no body clicks on them, but how did google find them? This is not evidence there is no links, just that no one has visited your site thought them

Yes you can, but how well multiple locations works, I don't know.

Its hard to get your homepage to rank in one location, let alone landing pages ranking in every location. Worth the try, but hard to do.

This is normal, try some other sites you will see that same pattern.

Bing stated they don't want every page, they don't want junk, they want only the important pages.

These pages may have links from other spam sites, you don't want them to return a 200.
You want them to 404, in joomla you can make the site use htaccess or not, make sure it dose and 404 the pages there.

Links send link juice to other pages, this is the same for internal links. It is not so much the number of internal links as the pattern of internal links that's is important. Using your internal links you can push page rank on to certain pages (Usually the home page). Lets say that you homepage ends up with twice as much PageRank as your other pages, then as your site gets more external links the incoming link juice will follow that existing pattern.

Reading this page will explain a bit better http://thatsit.com.au/seo/tutorials/a-simple-explanation-of-pagerank

Codeigniter is the php version of MVC, to be honest if you wanted to follow the MVC pattern Codeigniter would be my last choice, from a coding perspective it is ugly, from a performance perspective it is very slow, but all MVC patterns allow for good url structures, and you should be able to make a good crawlable site. Yost is a plugin to hide the short commings of wordpress, with a hand built site you should not have a need for such things.

As for the MVC pattern, the best MVC solution I think by far is ASP.NET MVC, but many will say ruby on rails. ASP.NET MVC makes good seo very easy.