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My redirects from old domains show up as back links, which makes sense--it is a case of a link from one domain to a different domain. So if you redirected all of those pages to your new site, you'd see a lot of links. As far as why it would be more pages than you had, take a look at the links and see what they are. Maybe you had different versions of pages that are showing up as separate links?
That is the only spam flag I get as well. The explanation is that: "Non-spam sites tend to invest in rich user experiences with CSS, Javascript and extensive mark-up. Accordingly, a large ratio of text to mark-up is a spam signal." I am not too worried about it--a fast site makes for a very good user experience, I think.
Oh, this belongs to a different thread: http://moz.com/community/q/chinese-site-ranking-for-our-brand-name-possible-hack
Is this part of the original conversation, or something else? Which sites are these?
Google Analytics has the option to capture demographic and interests information about website users. It is not as granular as what you are describing, but might give you a direction in which to start looking.
How does their organic search compare with their competitors'?
I spot check on a regular basis by taking a unique chunk out of a post, putting it in quotes, and doing a Google search on it. It's not comprehensive, but it is free. [And the main problems we have had with scrapers have been with sites that have taken huge portions of our content, not just an article or two, and a spot check roots those out.]
Sometimes people make pages like that as landing pages for PPC or other types of campaigns and then abandon them.
I found one like that on one of my sites once by noticing that a page I did not recognize was getting a lot of search traffic--I ended up integrating it into my structure with a new URL, and 301 redirecting the old URL to that new page.
If you think those might be good pages for you, different from similar pages you might already have, you can update them and do that as well.
If they are not especially useful to you, you could just 301 them to the most similar pages. [Are they getting traffic? I think Google must see something in them, if they are still indexed.] They probably wouldn't do any harm if you just leave them, but I'd take care of them anyway.
Sometimes when people link to you, they make a mistake (or even make up pages from what I can tell--I have seen some weird things). In that case, Google will still try to look for it and report back to you that it saw a link to such a page somewhere. [In Webmaster Tools, you will be able to see the referring site.]
What I do in a case like that is ignore it, unless it seems to be from a good site. In that case, I contact the site with a correct link and if I get no reply, I just create a redirect of the link to a relevant page.
A 404 is not a redirect, it means not found. So it is probably the case that someone linked to that page when it was up and Google is following that old link and not finding the page.
You mean a 301 redirect? If one of the duplicates is already 301 redirected to the other, like Jaime said, just mark it fixed. [Though if it comes back up, take another look at it, because it means that Google is not seeing the fix you think you made.]
As far as affecting your SEO, duplication can cause the less relevant duplicate to not show up in search but does not cause any penalty as such. [Though make sure your internal linking uses your correct and current URLs.]
Wish: Majestic/Ahrefs
I agree with Highland that this type of solution probably won't be your best choice.
How much of your traffic is actually mobile? Rand Fishkin shared this post on Google+, saying that Moz wasn't worried about making the deadline since they have very little mobile traffic.
Also, in this discussion here in Moz, Peter Meyers posted that this update is page-based, so if you have a smaller number of pages that are very mobile-crucial, perhaps you could fix those first, and then work on the larger fix for your website.
If you canonicalize the damaged product back to the original product, the damaged one won't be findable in search anyway, same as if you had deindexed it. In either case, people could still find it on your website.
And are you sure you cannot change the canonical? This support page seems to imply that you can.
Yes, it is indexed and shows up on the fourth page of results (#33, according to RankChecker). Sometimes a new page can bounce around in the rankings a bit.
Both Chrome and Firefox have incognito/private windows as a menu choice. A global way to do non-personalized search is to append ?pws=0 after the Google query URL. (And definitely be sure you are not logged in to your browser.)
What Google will show in the search results is partly based on what the person searched for. What was your search? (I see, based on the bolding, that it included camera and filters--were there any other terms?)
Also, what happens if you do an anonymous search? If you are logged in, you might be seeing things based on your history.
Here is a link with information from Google that might help.
If you have set pages to noindex, then Google will not index them.
Are you saying that you have other pages besides the ones you marked noindex that are not getting indexed?
Here is an article from backlinko that mentions something called the SEO Search Terms Tagging plugin, which sounds a bit like what you are looking for. The plugin was last updated over two years ago, but it sounds like you are looking for something from then.
My suspicion is that the plugin has not been updated for so long because of Google's (not provided) and is therefore probably not that useful. But the article also mentions a few other ideas [like checking out Google's "searches related to" at the bottom of the search results].
If you were using florida-car-insurance and then changed it to car-insurance, you should 301 redirect florida-car-insurance to car-insurance to ensure that any page equity that you may have built for the original page is preserved.