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The difference is literally that one involves liking a page and one involves sharing a page. They are two separate functions that can be done independently of each other, i.e. I can Share your article without having to Like your website & I can Like pages on your site but not choose to share them. A Share is the use of the Share Button to share/post a page, article, etc. to a person's timeline, a friend's wall, and/or the timeline of a page that the person's account is associated with as an Admin. Whereas a Like is someone clicking a Like button associated with a page, article, etc. stating that they like/enjoy it.

Are you able to place 301 redirects on the Old Domain pointing to the new one? If so, 1-to-1 redirects of pages from the Old Domain to their most relevant counterpart on the New Domain is a good step.

The keyword tracking tool is for organic rankings.

The SEO benefits of Tags tends to be negligible. Mainly they work together to help the user experience by tying together similar articles and increasing a visitor's time of site and pages viewed by offering them similar content that may draw their attention. The biggest problems with Tags (especially on Wordpress) is if you don't set them to NoIndex and have artciles to show Full instead of a Snippet on the archive page. When this happens you create a duplicate version on every Tag archive attached to the post, the Author archive, the category archive and the homepage. And a one-off tag with no other posts associated with it becomes useless because it creates more duplicate content without effectively tying your article to any other similar posts.

I almost always tell people with Wordpress blogs to switch posts to showing snippets on homepage and archives to lessen duplication, NoIndex archives, and (where possible) clean up & remove useless one-off tags that you don't think you'd use again and plan new content to add to the one-off tags you would use again.

Social signals can lead to a decent boost for a website. With the "downfall" of linking, many have looked to signals from social media sites as the new natural expression of a site's worth to their user base and as social proof of authority. It won't necessarily make you rank better in search results but it can be an integral part of the conversion funnel.

I completely understand wanting to target both. Since your title tag is too long, it seems to me that it would be better to choose one of the other to shorten it. Keep it in page copy and meta description where natural though... don't go changing that. But your title needs to be closer to 64 characters long. Plus Google takes into account pixel width to determine how long a title can be before it gets truncated.

As to the redirect. Link equity does get passed with a 301. As long as the links are relevant, authoritative, and/or not spammy then that's a plus.

As far as I know, in order to authorize the page you need to show that you are an Admin by logging in to a personal account associated with the page.

For the most part, trying to re-post your old content with a newer date in order to make it seem fresh when it isn't is really just an attempt to game the system. It may work somewhat in the short-term but its not a good long-term strategy. New, unique and relevant content would always be better.

Are they listed in Google Webmaster tools? You should be able to find out where they are linking from that way. Also, if they're 404ing and they weren't ever a real page and they aren't really being linked from anywhere then there's no real reason to stop it from 404ing. You should probably make a custom 404 to serve people that directs them back to your site instead of a completely blank page.

You could always test the link to see if it is really being used from the secondary navigation more so (or at all) than the main navigation link. Create a parameter and track it over a few months in analytics. That way you don't over-optimize in the interim but 3 months from now (or less, or more, really that's up to you) you can definitively say whether it is better to remove it or if leaving it alone was the correct move.

Just so I have this straight... if you go to Moz Analytics, choose your campaign, go to Search > Keyword Rankings in the left navigation, and choose the Competition tab... Your competitor is listed as Not In Top 50 for every single keyword you track?

I'm having a hard time following. A bit more info would be helpful if you don't mind. What pages are these? Who were they banned by? By "banned" do you mean they were penalized and/or removed from the index? What 3rd party app are you using?

I've had this issue twice in the past. Once was because of a conflict between All In One SEO and another plugin which was fixed by updating the plugins. The second time was after a theme change where it turned out the theme had an internal suite of SEO tools that were adding the secondary description which was fixed by shutting off those features. Without knowing all the details of your wordpress site, its a bit hard to determine the exact cause. Check that your theme doesn't have a function interfering with All In One and try turning off plugins to see if any of them are in conflict. Could be as simple as needing an update.

Last crawl I had the same problem. One of my campaigns dropped from 8000 visits to 0. The other campaigns were fine. According to Google Analytics everything was fine. I'm waiting to see if the current moz crawl happening for me right now fixes that issue.

Double-check they're in your competitor list without any spelling errors. You never know. The sheer amount of times I still type ,com instead of .com and somehow can't see the difference is staggering. Waiting a few days or for the next crawl can help as well if you've recently made changes. If it still isn't up and running after that, I'd get hold of Support and let them know there's an error.

I have done these and I agree completely.

Also, the bit about Canonicals to move a site and then 301 later was actually talked about at SMX by Maile Ohye of Google as a legitimate and good use for situations such as buying or taking over someone else's site as a means to pass link equity while also giving users a better experience by letting them know you are transitioning... giving them time to change their bookmarks instead of potentially causing them to bounce by sending them somewhere they didn't intend to go.

(though don't quote me on her saying anything about "link juice" or "link equity" specifically... it was about a year ago and its been ages since I've listened to my personal recordings of the session [and actually, i'm not sure I was even actually allowed to record while Google and Bing reps were speaking... but oh well])

General advice:
Do you have profiles on Social Media that you can share these pages to in a reasonable, relevant, authoritative and non-spammy way?

How are other corresponding metrics for the page looking? e.g. Can you work on improving bounce rate, time on page, etc.

Where are visitors going to after they are done with the page? e.g. Are you keeping them on your site? Where are they going on your site after the page? Are they leaving after they read? Are you offering enough opportunities for people to stick around?

Now.. Specific to your page I would look at the H tags. They aren't going to vastly improve your site but as far as I can see that page has two H1 tags. You should only have one H1 and can easily expand to include other H tags on that page.

It also looks like you could use more relevant, natural incoming links from a more diverse set of domains.

In the top right, click the symbol that looks like the head and shoulders of a person with some short lines next to it. Choose Billing & Subscription from the dropdown. You should be able to make all necessary changes from there.

Whether or not to exclude subdomains can only be set up when creating the campaign. After that, you're locked out those choices. As far as I know, you'll need to create a new campaign for your root domain and then leave "exclude subdomains" unchecked.

Typically a ccTLD is suited for that specific country/region. So having a .co.uk will make you more relevant to searchers in the UK but not for searches from say the US looking for something in the United Kingdom (unless they happen to be searching through Google.co.uk). This is not 100% always the case though but generally so. If you're attempting to globally reach people searching for that term, you'd probably be better off with a generic TLD.