I am not aware of anyway to determine if a site has implemented Google Webmaster Tools or not, as they could have verified it with by uploading a randomly named file, or through Google Analytics.  I would say if they are fairly large site and have Google Analytics (which you can determime by viewing the source code of the site) they probably have GWMT as well.

To determine if Bing Webmaster Tools are in use, you can go to http://example.com/BingSiteAuth.xml (replace the domain name) and see if the file exists.  If it does, then they activated Bing Webmaster Tools.  If the file does not exist, it either means that they never activated Bing Webmaster Tools, or they did and were smart enough to delete the file from their server.

Hope this helps!

Why not try to avoid the problem altogheter?  I assume the below line is site-wide:

If you remove the index, follow meta tag, your pages will still be indexed and followed.  Then allow your authors to decide on a post-by-post basis if they want to noindex or nofollow the page.

If all you plan to do is drop your links in social bookmarking sites, you're probably just wasting your time.  It's not likely that these links will be worth anything to search engines - even if they are followed links.  The time you spend building these links could be spend developing great content, or working on other link-building opportunities that would be more worthwhile.

As far as blog comments go - if your goal is to get backlinks, it's not a good idea.  These links are nofollowed and too many of them will look spammy to search engines.  If you are commenting to engage with the content author, that's a different story.  I often comment on other sites to engage with the content author and start a conversation.  I sometimes choose to include my website as a reference, but I often choose to leave it out.

I would tell your client to not worry about it.  I didn't know that GoDaddy was in the SEO consulting business now?

I found this as an explaination of what a GoDaddy SEO Checklist Stop Word means:

Words that are common do not help search engines understand documents. Exceptionally common terms, such as the, are called stop words. While search engines index stop words, they are not typically used or weighted heavily to determine relevancy in search algorithms.

It sounds like more of a warning to me.  I wouldn't worry about it.

The number of categories you have on your WordPress blog should accurately reflect the content you write about.  If you have a legitimate need for 50 categories, then by all means, 50 categories it is.  If your content all falls under 5 categories, then that is all you should need.

Essentially, let your content dictate how many categories your blog has.  Remember to look out for duplicate content, or pages with little to no content.  It's possible that you have a single blog post that is tagged to two categories - and those categories have no other posts attributed to them.  The category pages will then show short excerpts of the content (little to no content), and be essentially identical because the same post is tied to them (duplicate content).

I understand what you are referring to about having to hide certain elements on smaller screens.  Sometimes not everything fits or flows correctly.

When this happens, however, I try to hide design elements as opposed to text or links.  I'm also OK with hiding images.  If a block of text or a link seems out of place or doesn't flow properly, I will build a dropdown for it.  I'm sure you've seen mobile sites with dropdown navigation menus.

I wouldn't leave it to up to Google to interpret what you are doing.  Don't hide any links.

Moz has published a lot of posts on Link Building: http://moz.com/blog/category/link-building most of them have some solid advice.

If the structure is identical (I'm not clear on that from your post) then why not do a global redirect from the old content to the new content

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} !newdomain.com$ [NC]
RewriteRule ^(.*)$ http://newdomain.com/$1 [L,R=301]

This should redirect old pages to the same structure on the new domain, including images.