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Yes, you can adjust your mobile bid at the ad group level. Select the ad group you want to adjust by ticking the little box to the left of it and click the settings tab, then the devices sub-tab. You can adjust your bid by clicking in the in the "Bid adj." column.

I have never seen that. Exactly where in Google Analytics did you see it?

You cannot change it. Google does not allow Moz and other sites to use their data this way, so that is why Moz uses Bing. To get Google data, you need to sign up for Google Adwords and use their tool. (You do not have to be actively using Adwords, just signed up.)

Alexa rank is based on visits from people with the Alexa toolbar installed on their browser. This means that depending on what your website is about (thus how likely are users to have this toolbar installed) you may be getting lots of visitors that Alexa doesn't know about. (A lot of people do not consider Alexa to be a very reliable measurement.)

If their videos are on You Tube, You Tube provides analytics. https://www.youtube.com/analytics

I am not sure what you want to work around? Having the canonical tag on the canonical page? That is not a problem. Here is Matt Cutts on the topic: http://youtu.be/U8eQgx-njk4

I think Bing used to have an issue with it, but it is such a common thing to have a situation like yours where canonical tags are automatically put on pages that even that stance has softened, I believe.

[They are also handy to have on pages in case someone steals them outright--they will still give credit to the home site.    ]

The on-page grader lists the pages that rank in the top fifty for a keyword in one of your campaigns, so it is not the on-page grader that is choosing a particular keyword for a page, it is Google.

In other words, even though your "bracelets" page is not optimized for "rings", it still showed up for "rings" in the search results. And obviously since you did not optimize it for "rings" it did not do well for that word.

When you see a grade of "F" for a search term that doesn't apply to that page, you don't need to worry about it. Sometimes pages do rank for keywords other than the ones we are optimizing for. If you get a bad grade for a search term/webpage combination that are supposed to go together, that is the time to go back and re-optimize.

As strict as Google can be, I have never heard of them penalizing  anyone for something bad they used to do (but didn't get caught at) and have now stopped doing. I think they reserve their penalties for current bad actions. [Which is not to say you were doing something bad--we are talking about your wanting to be sure that it doesn't appear to Google that you tried something bad.]

In general, I think it's best not to disavow unless it is an extreme situation. As Google itself says: "In most cases, Google can assess which links to trust without additional guidance, so most normal or typical sites will not need to use this tool."

Since the links are using 302 redirects they are not passing any link juice, so I can't imagine that you'd be penalized for them.

As far as the question of subdomain vs subfolder, Matt Cutts said to do whichever is easiest: http://youtu.be/_MswMYk05tk

However, there was a question about that topic here on Moz a few months ago, and Rand Fishkin "strongly urged" a single subdomain (which is also my own preference): http://moz.com/community/q/moz-s-official-stance-on-subdomain-vs-subfolder-does-it-need-updating

And for www vs not, you will have to 301 it one way or the other and there is generally very little link juice lost with a 301 so if no www is better for your brand, I would go for it.

I was using the DOM inspector in Firefox (right click on the empty area to bring it up).

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You have 191px of padding on top of your div "inner-page-wrap has-no-sidebar clearfix", with the grey box and photo of three people in it. Eliminating that will eliminate whitespace above it.

Do they use canonical URLs on their website? Do the cross-posted blog posts have canonicals that point back to the originating site? If so, the duplicate content should not harm their website and their website should rank above the bigger players for their content (though not necessarily--Google works in mysterious ways).

In general, it is a good idea to keep your best, fresh content on your own website but sometimes it can be good to get the added exposure of a high-traffic website, assuming that it is clear where the content originated.

You don't need a special tool, just go to whois.net and check the domain.

Yes, I have been having the same problem.

[There was another discussion about this recently: http://moz.com/community/q/analytics-account-will-not-stayed-connected-listed-fixes-do-not-work ]

The reply I got from Moz said in part: "We are trying to improve our relationship with Google so this connection can become less finicky." So it does sound like there is an issue there.

The date on that post is 2010-- a lot has changed about Adwords since then!
Here is a more recent post, hot off the presses: http://www.business2community.com/marketing/google-updates-adwords-keyword-planner-tool-advertisers-need-know-0861602

No, my tokens were fine. I just reconnected it several times till it stuck.

Yes, my account is connected right now. When this has happened before, it was on-and off for a little while, then on for a long time, then on-and off...

I did receive a nice response from Moz Help, which said in part: "We are trying to improve our relationship with Google so this connection can become less finicky."

So it sounds like this is perhaps a problem with the connection between Moz and Google in general?

You can still use the Adwords Keyword Tool (now called the Keyword Planner). You do have to create an account, but you do not need to be running any ads. Wordstream also has a Keyword Tool, through the free version is limited.