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Let me just start with saying...stop and take a step back.
Above you mention a bunch of outdated (directory submission) or just bad techniques (link exchange). I suggest you take a look at the SeoMoz beginners guide first to see what is all involved in SEO and than start from the ground up
Put your head down and get some links in the good way. product reviews, service reviews, run some contests etc.
Then look over your site and your competitors. There always is some way to battle it. For example, if you are on page 1 and they are higher, are either of you using schema markup? Start thinking outside the box and thinking about CTR. You don't have to be #1 to start taking the bulk of the traffic. Make your result more attractive. Offer free shipping? Append it to the end of your title tag
All depends how you can categorize them. I have done/worked on sites that are more than 2 clicks and they do just fine with revenue.
Do the 20 categories have any parent categories you can put them into to put in the navigation? Also what about drop down navigation. This can allow them to dive deeper if they want or browse if they need to.
Can you give me some examples or a screenshot?
You can use crawlers like xenu or screaming frog (http://www.screamingfrog.co.uk/seo-spider/)
How about spending a few hours and read http://www.seomoz.org/beginners-guide-to-seo as I can ensure you that even the newb can learn something that is better than spending 1hr of SEO consult as that agency seems pretty expensive at $250hr
Depending how customizable your platform is, you could if discontinued, 301 to next level page in the breadcrumbs. Which would be a category/sub category page
If he is debating the budget of 1hr or spending same $ for a paid link, he isnt hiring a firm. He is trying to get gains from a small investment. His time is better spent learning some basics. Most sites are so bad that simple changes and learning how to structure content can get him gains in the near future.
Facebook shares and facebook likes are different. As someone can share a post they see on a friends wall and it is not added to that page's like count.
If you want to check the like count for certain urls quickly, I prefer to use the excel plugin for SEO
http://nielsbosma.se/projects/seotools/
Just do not try and do a few thousand urls as it will take a bit.
If your company is Acme Inc. any branded keyword is considered variations of your company name:
Acme
Acme Inc
Amce Inc
etc.
You figure out what regex works in google analytics or whatever analytics platform you have so you can filter these into groupings of branded and non branded when looking at traffic reports.
Would rethink the design of the page. Are there any better ways to design the page? Could you leverage lightbox? Screenshot the videos and have them target=blank? Granted not every solution is ideal but if you must cram a ton of things on a page that will cause insane load time you also have to consider the fact of if it is a long time period, it will tick people off and thus not be as link worthy as you may think.
People on the internet have practically 0 patience...just remember that when coming up with your plan.
Have you isolated it down to a page type, or specific urls?
If not build out an excel file with the following as columns and then pivot it out:
Then pivot the above and report back
Judging by what you said here "Yes, my focused anchor text has more links than other, but i've done very few links so far, like 10 bookmarks, 2 directories, 3 press releases, and a few article submissions. So far all the links are with DA 80+."
That is not good link building really. Its crap. yes they may have high DA but its directories. Whatever your niche is, you need to get good resources to link to you not directories. What I would do not only for yourself but your competitors is run an anchor text diversity report here and there to keep an eye on it. You can do this by exporting your 301+followed to root domain into excel and than doing a pivot pie chart to keep an eye on this.
Also make sure to take a look at the beginners guide here http://www.seomoz.org/beginners-guide-to-seo as it is a good start if you are new to seo
Going after the head term and you can always use some onsite and link building to rank for the other longer tail terms. Also try leveraging user reviews if possible (and indexable). Why not see if you can get people to leave reviews on how your prices are so good its like always buying on sale compared to competitors. Get people to link to this page and I would not be surprised if you can get it to rank for your other targeted phrases
What is the site built on? If wordpress, check out wpengine (no affiliation). Just saw this post and wanted to respond as I had tons of downtime when I migrated a site to a shared environment on another host. Site kept having downtime no matter what I tried with support. So you can imagine the frustration and how this can impact the business not just from a search perspective. I think the question here is how stable do you need something. Does shared work? Yea sure. But if you are putting something that is the core of your business on a $4.95mth host, than you get $4.95 worth of insurance.
First questions to ask are what platform is the website on and are you sure analytics is installed properly? I like to get those out of the way first before you start to dive into more info.
And is this isolated to specific pages these keyword landing pages?
Run a custom report in google analytics by landing page with filter only containing those affected keywords
Assuming you are in the eye glass business, why not find bloggers and give some product away to those bloggers for product review posts? I would stay away from any paid blog networks.
Yes you can 301 a page that has 301s. Just do not want to cause a 301 redirect loop. But the more important question here is why you keep changing urls based solely on keywords. You hint at it above. You do not need to keep changing your url over and over based on whatever the head term is. That is silly and if you think how google would want, this does not make sense. But that's just my two cents.