Hi William,
Did you try out Ontolo meanwhile?
Gr., Keszi
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After some research made, I have found the following code, which could be implemented in the theme's functions.php:
function rel_next_prev(){global $paged;if( get_previous_posts_link()){?>
}if( get_next_posts_link()){?>
}}
add_action('wp_head','rel_next_prev');?>
Try it out, and let me know when it is live. We can then check if it works well or not.
Gr. Keszi
If the admin subdomain is used for any testing purposes, then I wouldn't redirect it. If there is no specific use for it, you could do a 301.
If it is used for testing purposes, then you could:
I hope it was helpful.
Gr., Keszi
Like Linda mentioned it, I would also keep it under one domain. What you could do is to present the cons and pros of each version, maybe you can convince your client 
Basically the two websites from content point of view are going to be similar in any way?
Hi,
I'd completely deny access for robots to the subdomain. For this I would create a robots.txt for the subdomain (place it in the folder of the subdomain) which would state the following:
User-agent: *
Disallow: /
This way your content from the subdomain won't be crawled by search engines -> no content duplication issue for search engines.
Gr., Keszi
This is true.- In case of duplicate content.
But until now we didn't talk about same content on the secondary website. This is why I have asked him to give us a little bit more information. 
Hi,
I do not really understand the question. Is the secondary site on a separate domain or are you implementing it on the same domain?
Could you give a little more information? So we can give an easier answer 
Gr., Keszi
Each search engine has it's own search algorithm. In some cases things are similar, but I do not think they can be correlated.
Hi David,
Isn't it possible that your website has been effected by another Google algorithmic update, while the manual penalty?
Gr., Keszi
Ivan, correct that homepage is a "static page", which has a custom template in your theme directory.
That template has a loop which is going to show your latest articles on the homepage. That's part of the file you need to edit.
Gr., Keszi
So the question really is, what kind of page template does the homepage use in order to pull in the data. We would need to modify that in order to put in the pagination.
P.S. Sorry for the late reply.
I am not 100% sure. For that I would need to have a look at the php code.
For sure, now it is not implemented.
Usually Wordpress SEO by Yoast implements this automatically when we are talking about category/tag/date/etc. archive pages.
In case of the homepage, I do not know personally where to implement it - I'd need to see the code for it. 
I believe what you are missing is the pagination markup link rel="prev"/rel="next". This is why all the paginated content is indexed, although you have a canonical link set up.
Gr., Keszi
I do not believe that having the same text in h1 and title tag could cause any issues. For example we can see a lot of Wordpress websites rank where the title wasn't rewritten. There in most of the cases H1 and Title tag are exactly the same. (or differ only in a | Brand in the title)
That's a personal opinion.
Gr., Keszi
I personally do not see anything wrong with the code.
Maybe you should try that test, change it drastically then go and fetch it from Google Webmasters Tools. Let's see what happens.
I'd test it with one page, then fetch it from Google webmasters tools.
If the test works, then it could be applied to all of the problematic pages.
Hi Amelia,
IMO you should write an email to the help team: help@moz.com. That will be the fastest way to resolve your issue.
I hope it works out well for you. 
Gr., Keszi
Hi Fernando,
It should not have any issues from SEO point of view.
We are using the same technique at a client's website (to distinguish easily a hungarian and a romanian version which are not the same at all - so a multilanguage implementation wouldn't have been benefitial), and both version are working fine.
So I would not worry too much about it.
Gr., Keszi