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Screaming Frog
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Ahrefs & Majestic
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GA & WMT
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Copyscape/Siteliner
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Excel SEO Tools
And if I could have one ... well I just got Buzzstream so I have it - but haven't jumped too far in yet.
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Screaming Frog
Ahrefs & Majestic
GA & WMT
Copyscape/Siteliner
Excel SEO Tools
And if I could have one ... well I just got Buzzstream so I have it - but haven't jumped too far in yet.
Actually, before you redirect ALL errors to the homepage, please do some reading on that tactic:
http://www.rimmkaufman.com/blog/seo-and-404-pages/01022013/
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=93641
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=2409439
http://googlewebmastercentral.blogspot.com.au/2011/05/do-404s-hurt-my-site.html
Google specifically says (page 13)
Avoid not having a 404 page at all.
Finally:
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=83105
Use a 301 Redirect to permanently redirect all pages on your old site to your new site. This tells search engines and users that your site has permanently moved. We recommend that you move and redirect a section or directory first, and then test to make sure that your redirects are working correctly before moving all your content.
Don't do a single redirect directing all traffic from your old site to your new home page. This will avoid 404 errors, but it's not a good user experience. It's more work, but a page-to-page redirect will help preserve your site's ranking in Google while providing a consistent and transparent experience for your users. If there won't be a 1:1 match between pages on your old site and your new site (recommended), try to make sure that every page on your old site is at least redirected to a new page with similar content.
Google does not recommend this tactic and says "Avoid." That's enough for me. I don't know how to help you with the Mod Rewrite but I wouldn't 301 your 404. 
The problem with asking SEOs about DMOZ is it used to be VERY valuable. Now it's not.
But it does still retain some value. Consider a $500 per share stock that falls to $50 per share. It's going to feel practically worthless but it still has more value than MSFT stock ($43 a share today.)
So the relative value is "massive decline, don't recommend" but the true value is probably "it has some value, is easy to create, but may never go live. It's 20% a $50 share and 80% a $0 never-goes-live share.
Whether that's worth your time is up to you.
Yeah, Google used to scrape Yelp but was under investigation by the FTC for doing so. I don't think they still do though some of the older data (like 2011, 2012) may still be there. I can't imagine they're still doing it.
You should definitely start with an intense discussion we had on Inbound about subdirectories/subfolders. Not because you're asking the subfolder question but rather there's a LOT of really good info about subdomains for SEO.
In general, most people (but not all) agree that subdomains act as their own separate websites. Since all 3 of your options are basically the same (subdomains) then we can just jump ahead a bit.
Choice 2 seems ... redundant ... to me? I don't see the benefit.
Choice 1 vs 3 comes down to do you use your own domain or a throwaway. I would suggest that since you don't know how Google will treat them in the future, a throwaway is probably preferable. I know Wordpress uses a simple subdomain, as did a lot of older CMS' but I think the trend now is to not give Google hardly ANY chance to mess up your SEO by combining it with others. Even though that's not how it seems to currently work, that could change tomorrow. If it's on a separate, throw away domain it really can't be.
The only concern with that is to make sure you don't interlink all your client sites to yours through things like a footer link. You could very quickly and very artificially bank up tons of external links with a simple Theme by Our Company link. It's on a separate domain so those would add up very quickly as external links.
Generally speaking, if you're concerned with anchor text because you control it, those are the wrong links to be building.
Exact match anchor text depends on whether your anchors match each other for your target keywords. If you have 100 links and 90 say "cars in Boston" you're going to take a beating. If 5 are "cars in boston" and 5 are "boston cars" and 3 are "Hyundai Boston" and another 10 are your brand? Not so much, really. You can also build partial match links.
and this: http://www.webmarketinggroup.co.uk/Blog/the-truth-about-exact-match-anchor-text-1760.aspx
Hope that helps!
The key point to me in any anchor text discussion is this: Google doesn't want you to control your IBLs. Most sites that link naturally will not use the same anchors over & over.
If your link profile is natural and you don't control a whole lot of it, yes anchor text is very valuable. If you control most of it and you're adding to the same stuff over & over, it's very bad for you and can result in your rankings dropping.
This is the exact reason SEO can be so difficult. The same link, the same anchor, the same page on the same PR site linked at the same time = everything 100% the same = can still have two very different effects on a business depending on what the existing site, profile and anchors look like. So there's no clear answer to many SEO questions like this. The answer is "it depends."
The title length question is easy enough - it's DSA (dynamic search ads.) They basically insert your search query into the title. http://www.google.com/ads/innovations/dynamicsearchads.html
I've seen some pretty long ones with DKI/DSA.
Not sure on the ad block question - I don't have that on any of my few test searches, even the obvious dynamic keyword ads.
http://www.beansbox.com/blog/understanding-dynamic-keyword-insertion
Check out the source code - it mentions "dolls" almost 200 times. I know we (as humans) see the page itself but Google doesn't read it the way we do. Jump into the code and check out what Google is reading.
Also, you've bought links at some point in the past. Depending on what you cleaned up, things could still be in strife. According to Ahrefs, you have almost 2k links with about 550 referring domains - that number of referring domains tells me straight away that something is dodgy. 33 incoming .org domains, 23 .de domains, 10 info and 8 russian spam...
It's not really a shock that this hasn't recovered, tbh. There's a LOT to go through. Without diving into your WMT, I can't tell you what Google sees that Ahrefs doesn't, as well.
A lot of the pages are very small. I ran a quick Screaming Frog crawl on it and the page size was in general just a sentence or two per product. You're probably dealing with a bit of thin content as well.
We have had two massive clients (one well-known real estate company, one international brand) both manually penalised for these type of links so I would say you should probably start working them out of existence before you get penalised as well. (If I had been a Google reviewer instead of an SEO guy helping me out, you'd have a penalty. All it takes is the wrong set of eyes on the site.)
As far as your below question re: historic link profile, it's hard to say. You never know what Google sees, when they first saw it and how much they value it. I believe links get less valuable over time so to some extent it's not the be-all, end-all but if those links have been only just crawled in the last few months even if they were created 10 years ago, they may be just as valuable as one created today.
It may be too late to help you but in case someone else has a similar problem:
Repost the article (or much of it) on Facebook.
301 redirect your viral post to the new post. Images, post, content, etc. won't load at all - visitors will be directed to a server that can handle the load.
Also, by directing to your FB page, you may have more likes, more shares and definitely more fans by the end of it.
Gosh, that's a HUGE site. Are you having Google crawl parameter pages with that? If so, that's a bigger issue.
I can't imagine the crawl issues with 500M pages. A site:amazon.com search only returns 200M. Ebay.com returns 800M so your site is somewhere in between these two? (I understand both probably have a lot more - but not returning as indexed.)
You always WANT a full site crawl - but your techs do have a point. Unless there's an absolutely necessary reason to have 500M indexed pages, I'd also seek to cut that to what you want indexed. That sounds like a nightmare ecommerce store gone bad.
Well, B is definitely the better idea. Both would most likely help your rankings (depending on existing link profile, etc.) but B is cleaner, though harder. I would prefer to go down that path if you have the resources.
Also, if you buy the domain, those backlinks are disconnected until you reconnect them. So don't forget to ping the good backlinks if you do decide to go down the A path. Download all the links you can find, ping them in a tool like pingfarm and they seem to "reconnect" and repower the domain. Google just has to crawl those old pages, see the link still exists and you're good to go.
(Again, B is a preferred choice...but in the interest of information, A would probably work.)
Got your PM & replied. You have mail. 
The blog posts themselves are all set to nofollow in the meta robots tag on each page.
The backlinks are a problem. You have some obvious link networks on there, specifically:
top.ind.in options.pw submit.pw aahana.co.in toplist.space toplist.ws toplist.co.in url.firm.in alexa.in.net toplist.in.net
All of these are on the same IP. That's a whole lot of domains on one IP address that all link back to you - and that's not the only network set. I'm not sure how much the sitewides from zeldaeurope.de and vgchartz.com are helping you either. The zeldaeurope is listed as an "affiliate" with almost 80,000 dofollow links. Google may be seeing that as a paid footer link.
Homepage is a bit slow - 2.9 MB and over 8 sec load time on Pingdom.
Content - mentions the 3 main keywords - "zelda" "triforce" and "game" or "gaming" at least 300 combined times in the code. It's pretty high, I think. Especially given that your title has Zelda three times as well. We've found that 1 is best, 2 if you're separating with pipe - but 3 is usually too much. So between the two, a bit of a Panda bite.
I also see two major ads above the fold. One is for Forex, the other for a bank. A refresh shows me Careers Australia & a cloud security company. I mean the ads aren't even closely related. A gaming site with a big forex ad tells me there's an issue somewhere, as well.
Sorry I can't go further but as Matt said, you could always get someone to help you out outside the forum.
Winning, even if temporarily, is sometimes a very big money proposition. If the money is there, I would start a second site. Run the main site the best way you know how. Run the second site as a churn & burn if the money makes it worth it. It really depends on the outcome you're looking for.
Also, if you want to really rank it, use this as a test opportunity. Test a few different mini-sites in the niche. See what works & what doesn't. Find a good way to rank & push with that WHILE you build the main site properly for long-term ranking.
At the worst, the site never really ranks. At best, you have both a temporary AND long term win in the queue.
(Someone will inevitably mention that Google may dislike this theory of mine so you may want to build the two sites with separate "everything" just in case - but I think you'll be fine. I just want to offer something outside the box. Whatever you do, discuss with the client first & give them a few options.)
We've done this on all disavows lately - submitted to both. We haven't seen any negative effect but we've seen cases where it SEEMS like there was a positive effect. It's very hard to say because obviously disavows aren't instant and you aren't always 100% sure what you can attribute to which part of the process.
In my experience I would submit it to both.
Tulane.edu, tulane.net, tulane.org & about 15 other sites link to the non-www version.
Worcester, ETSU & AIC (along with 3-4 others) link to https version
Also:
etsu.edu/crhs/aslp/audiology/resources/default.aspx is 404
lakeerie.edu has https issues of their own so the page is missing
In my full look I saw 145 edu links to your site. Of these, hastingscenter looked like it was removed. That leaves 132 unique EDU links.
Of the 132, 108 are not indexed according to SEOTools.
Of the remaining 24, 9 are Worcester, Tulane or AIC.
Accounting for duplicates I see ODU, Setonhill, HamptonU, Pihma, mmm.edu, stanbridge, ccac, lec.edu and lakeerie.edu that should be in Search Console.
You should see some of the remaining 15 in Search Console though. Not sure why you aren't seeing as many are older links.
You have two titles.
<title></span><span class="webkit-html-tag">Ergoback- Neutral Posture Seating | Ergonomic Office Chairs | Rochester, NY</span><span class="webkit-html-tag"></title> (75 characters)
<title></span><span class="webkit-html-tag">ErgoBack.com Home Ergo Back - www.ErgoBack.com</span><span class="webkit-html-tag"></title> (46 chars)
So you have one title over 70 and a total of about 120 characters in the <title>tags. I would guess those are your two problems.</p> <p> </p> <p> </p></title>