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As far as I can see, if the content is exactly the same on both the .com and .co.uk sites and you intend to keep it this way for the forseeable future, then there is no point maintaining both. Put all your efforts into developing and maintaining the .com site. Not only will this ensure that you are able to build the authority of one domain, it will also ensure that all your social media activities will be for the one site rather than sharing both .com and .co.uk URLs.

Alternatively, if you want to differentiate your content slightly for a global and a separate UK audience then hreflang across the.com and .co.uk sites is the way to go.

In my view there is no issue with you using your default for en-us. It may not be necessary to reference en-us in the code as Google will know that www.mysite.com is your default for English speakers in the US in any case, but there is certainly no harm in leaving that line in there.

As to your second question, I always reference every alternative version of a page in the hreflang including the page itself, so in the example you have included  code on the page on the UK site. This is perfectly fine and is how I have always implemented hreflang when dealing with pages that are similar but intended for different countries/languages.

Sites that optimise the mobile experience will enjoy better rankings. That doesn't have to be a responsive site - it could be delivered on a separate mobile version or by dynamic serving. Clearly if you are providing your mobile visitors with an experience enhanced for mobile devices then you will be rewarded for that. A users who comes to a site from search which provides only a desktop version of the site and finds it virtually unusable will inevitably click back immediately - sending to Google the signal that their search query hasn't been met by that site. Optimise the user experience for the device the user is using - remember responsive isn't always the best option for user experience.

Webmaster guidelines specifically request that you prevent crawling of search results pages using a robots.txt file. The relevant section reads: "Use robots.txt to prevent crawling of search results pages or other auto-generated pages that don't add much value for users coming from search engines."

There was a great Moz blog post on the whole re-direct issue by Cyrus Shepard which is well worth taking a look at.

By all means provide a link to the sponsor but absolutely make sure you 'nofollow' that link. Here's the relevant link to the Google Webmaster blog where they state why you should avoid selling links that pass page rank.

It doesn't make sense to noindex your mobile pages, after all, surely you want them indexing especially if some of your pages are not exact duplicates of your desktop site pages. If you are concerned about the appearance of duplicate content, then use a special mobile rel='canonical’ tag. You find plenty about it here where essentially the advice from Google is as follows:

To help our algorithms understand this configuration on your site, we recommend using the following annotations:

1. On the desktop page, add a special link rel="alternate" tag pointing to the corresponding mobile URL. This helps Googlebot discover the location of your site's mobile pages.
2. On the mobile page, add a link rel="canonical" tag pointing to the corresponding desktop URL.

You'll see an example of implementation on the page if you click on the link I've added. Hope this helps.

Is it possible that some of the pages have inadvertently had a noindex meta tag added to them or that certain pages are blocked in error by your robots.txt? Without your site URL it is very difficult for any of us to ascertain the issue.

Same here Gordon. All our sites have experienced a drop of around 2 in DA.

When did you submit the new sitemap? I have known it to take more than a few days for the pages submitted in a site map to be indexed.

As a separate point I also noticed that many of your pages have the same tag cloud on the right of each page which can be seen as keyword spamming. Take a look here to find out why it may not be helpful to your pages and ability to rank.

I can't see any reason why you would want to nofollow links to your own social networking pages. They are very much related to your site so why not pass pagerank to them. As Takeshi rightly points out, if you nofollow them then any pagerank they might have got from your home page just evaporates.

I think the best thing to consider is what is best for your users rather than a search engine. If having a mobile version improves their user experience then great.

Google have expressed a preference for responsive over mobile but again you have to think are your users best served by a mobile (and possibly scaled back version) of your site.

There have been some great blogs on Moz on the whole mobile issue which I think you should check out.

http://moz.com/blog/seo-of-responsive-web-design

http://moz.com/blog/how-to-optimize-a-mobile-site

http://moz.com/blog/mobile-seo-process

Have you had a look in Webmaster tools for any issues? Any unnatural links warnings? Have you lost any significant backlinks? There could be any number of reasons, be it Penguin or Panda - without more info people will struggle to give you suitable solutions.

Definitely your language used in your URLs should reflect the country/language you are targeting. If, for example, you saw a search result in US SERPs but the language URL was in Spanish, I'm pretty certain most people would be less inclined to click on the result.

This was covered by Matt Cutts in a blog post way back in 2007 but the advice is still the same as Mik has pointed out. Search results could be considered to be thin content and not particularly useful to users so you can understand why Google want to avoid seeing search results in search result pages.  Certainly I block all search results in robots.txt for all out sites.

You may lose 4% of your search traffic in the short term, but in the long term it could mean that you gain far more.

Personally, I'd focus on your own site and keeping your content quality and unique. In the past we have had our fingers burned by syndicating content to other sites and finding that they end up outranking us for our own content. While the referral traffic can of course be useful, you have to weigh up whether the benefits of referral traffic outweigh the negative impact on the ability of your own site to rank well.

If you decide that referral traffic would still be an avenue you wish to pursue then perhaps you could consider providing content that is considerably different from the version that you keep on your own site or at least making it just an abridged version. Also make sure you publish the content first on your own site before allowing it to be published elsewhere.

Google will not view translated content as duplicated, rather it will view it as rather spammy since auto translations are far from perfect and the translated content often appears as a very 'broken' version of whatever language you are translating into. Ideally, while I appreciate it can be pricey, do not use autotranslate tools but instead have content translated properly by a professional.

It really depends which markets your client is trying to target. If their target market is UK only then the .co.uk is perfectly fine. If the .com is available then it would do no harm to purchase it to save a competitor getting hold of it and outranking for the domain/brand name. You could simply redirect the .com to your .co.uk site.

Alternatively if the target is wider than the UK then it becomes increasingly difficult (though not impossible) to rank with a .co.uk in other countries. Hope this helps.

Redirecting multiple pages to one page is ok so long as there is relevance, after all you want to send your users to somewhere that is of use to them. What you don't want to do is just point all 404s to one page such as your home page.

I think the whole redirect issue was expertly covered by Cyrus recently in this great blog post.

You could make use of differentiating each of the title tags with use of page 2, page 3 etc but in addition if you really want to capitalise on the strength of the pages you could make use of the rel=next  rel=prev mark up to give a strong indication to Google that these are a paginated series. This will consolidate the indexing properties across all the pages.

Look at the following example lifted from Google webmaster Central

Let’s say you have content paginated into the URLs:

http://www.example.com/article?story=abc&page=1
http://www.example.com/article?story=abc&page=2
http://www.example.com/article?story=abc&page=3
http://www.example.com/article?story=abc&page=4

On the first page, http://www.example.com/article?story=abc&page=1, you’d include in the section:

On the second page, http://www.example.com/article?story=abc&page=2:

On the third page, http://www.example.com/article?story=abc&page=3:

And on the last page, http://www.example.com/article?story=abc&page=4:

By all means make each of the titles unique, but also connect them all in the series by implementing rel=next rel=prev.