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You also can use JSON-LD to add this in site w/o messing with HTML. Just refer to their documentation because it can be placed everywhere - in HEAD or in BODY but wasn't visible.

Well - this is easy win. But you need to ask yourself - should you put products in homepage?

In Woo you can easy duplicate /shop page with / (homepage). And when i go in some site i want to know about their company, best (best-of-best) products, etc. This is huge niche for A/B tests. For example - you can put some promo on some products and drive traffic to them. Or company innovation, or company news, etc.

Imagine Amazon (just example) if you visit them did you get ALL of their billion products on their homepage? Or if you visit newspaper did you get ALL their news on their homepage?

Only change between /shop and / is one image in homepage in ATF.

So - yes, you can canonical them, but then you will miss much better opportunity in CTR or CRO.

I don't know what kind of Woo + WordPress + theme you use. But you can download everything into separate folder and use tool to find text in all files. You just need to look who is responsible for "schema.org/Offer" adding into HTML.

Here is shoot in the dark:
https://webdesires.co.uk/blog/add-schema-to-woocommerce-products/
you just need to reverse this change.

As i said - it's just guessing. Can be also in plugin somewhere.

Yes! I have tested them in this one:
https://www.youtube.com/watch?v=5ip03xNfpwg

CTR was 6.36% and closes are 9.09%. I know that they're not "best-of-best" annotations, but definitely helps. But video is strange because have long intro and one of note is for jump inside of video where action begins. I'm trying to implement also "cards" in YouTube videos to see their performance too.

Here is example of Rich Snippet w/o offer (with price):

ACME
  Executive Anvil
 
  Sleeker than ACME's Classic Anvil, the
    Executive Anvil is perfect for the business traveler
    looking for something to drop from a height.

Product #: 925872
  4.4 stars, based on 89 reviews

As you can see this code can be validated and works OK. Now you need to go back in Woo and make "patch" to remove http://schema.org/Offer where is price located. OR temporary disable them.

Real case... almost 10 years ago SEO manager in some company was flying to their HQ just to explain why their PR was dropped from 6 to 5. C-level execs wasn't happy about that.

Now fun part - impressions, CTR and visits was increased during that update.

True - potential impact can't be seen. But we have few awesome articles about this:
http://www.stateofdigital.com/optimising-urls-seo-ux/
https://moz.com/blog/site-architecture-for-seo
https://moz.com/blog/ugly-seo-mess-recovery-case-study <- checkout "flat structure"

So you now don't have silo structure in your site and he didn't works works. There are many authors about silo structure - Yoast, Bruce Clay, Glenn Gabe, etc. I can suggest to educate little bit about that and implement some structure. Of course redirect 301 old pages to new ones.

Same here... first goes up and now (this week) goes down. Probably they tweak something like fine-tuning algos.

True - i just joining and #WTF seeing such results.

Wordfence? RU serious?

This plugin can serious hit your SEO performance because their settings. For example - you return error to GoogleBot...

Maybe can help you?

I have talk about this in WordCamp Bulgaria 2015 about this issue "Accelerating WordPress":
https://2015.sofia.wordcamp.org/session/ускорение-на-wordpress/
Drop me URL in PM so i can evaluate WP and i will post here (for free) few ideas and steps for this.

Why you didn't put this in inbound.org job board? Or find someone, somewhere and outsource part of work. If you're in doubt look on WordPress team structure. Seems that distributed teams and members works not bad as regular company. Or create Facebook or Twitter ads about that. Be a creative and tricky. Can be SEO test for example. Or make LinkedIn ads.

As you can see there are many ways to find someone.

There are two reasons that i still didn't move to HTTPS:

1. Twitter counter
2. Facebook likes

Since Twitter counter was killed only remain likes. But i will move soon w/o waiting for them. Only G+ follow 301 redirect and pass links.

That's right. JSON-LD doesn't require change of HTML compared with Microdata and RDFa. And this is one of answers why JSON-LD is beautiful. Second is because you can make changes in JSON-LD without touching HTML. Like adding new fields, parameters, etc.

About placing. I think that this can be just on home page. Placing in each page is pure rich snippet spam.

If you wish to see performance of KWs or pags you can see few tricks from today post in Moz:
https://moz.com/blog/single-best-seo-tip-for-improved-web-traffic
Yes - SearchConsole is heavy involved in process.

Not set

The ‘keyword’ (not set) simply identifies traffic that doesn’t arrive via a particular keyword and hence may not come via any search at all. This includes traffic coming from email, referral sites, or even things like Google Images. The latter might be confusing, but it helps to know that visitors coming from Google Images and Google Maps are classified under referrals with the source google.com, not organic search. Because keywords are automatically set for search traffic, the (not set) keyword will never appear in your organic Search reports, so it is likely something you won’t have to worry about. Don’t consider this one in light of keyword performance!

Source: http://www.gravitatedesign.com/blog/not-set-not-provided-mean-google-analytics/

Not set

The ‘keyword’ (not set) simply identifies traffic that doesn’t arrive via a particular keyword and hence may not come via any search at all. This includes traffic coming from email, referral sites, or even things like Google Images. The latter might be confusing, but it helps to know that visitors coming from Google Images and Google Maps are classified under referrals with the source google.com, not organic search. Because keywords are automatically set for search traffic, the (not set) keyword will never appear in your organic Search reports, so it is likely something you won’t have to worry about. Don’t consider this one in light of keyword performance!

Source: http://www.whereoware.com/blog/not-set-vs-not-provided/2013/05/

This is in Acquisition, Campaigns, Organic keywords. If you're talking Acquisition, SearchEngineOptimization, Queries - this works different, see text in below.

So - in general Analytics can't figure keyword there. But this is not how GA should work. You should tracks your KWs in Google SearchConsole. There is "SearchTraffic" -> "Search Analytics" with all impressions, clicks, ctr and positions. There you can make report for web, image or videos. You can split traffic by countries, pages, devices (desktop, tablet, mobile) and much more. Here is link:
https://www.google.com/webmasters/tools/search-analytics?hl=en
but there you must add your site and verify it.

There are few likes - likes to Facebook Page and likes to Web Pages. Since i don't understand your question will explain both cases.

1. Facebook Page likes will be not touched.

2. Website Pages likes will be lost will be lost. Facebook bot will follow 301 redirect but will not pass likes to new url.

There is "hack" Like button like this:

if you change data-href in this example - you will change URL for liking and counter can be saved. So you can implement this technique and wait for better times when bot will follow like values to new url. If this happen anyway.

The case is when you have special website that serve different versions of site based on user agent. So in this case you want to see what GoogleBot could retrieve from your site. This also can assist you in mobile redirects too also based on user agents.

In only one way where can't help you - it's responsive web because there bots see only one version of HTML.

Spam score isn't only backlinks:
https://moz.com/blog/spam-score-mozs-new-metric-to-measure-penalization-risk
https://moz.com/blog/understanding-and-applying-mozs-spam-score-metric-whiteboard-friday
and here you can see all of them:
https://d1avok0lzls2w.cloudfront.net/uploads/blog/5515baf4a31ab5.95588612.gif

So you need to fix them. Here is another example:
I visiting:
http://www.cornerjob.com/robots.txt/company/  <- please note there isn't 404!
and i get:

This tell bots that your site have only one page and it's homepage. And / it's 302 to /en/.

That's why you have such score. You need links too (no-followed).

I just crawl your site with desktop crawler and found that you have just 67 internal HTML files. I know that there is export from Joomla and import to WP but in reality things wasn't as advertised. So here is mine idea:

1. Keep actual Joomla as-is for now
2. Make copy of site with some web site saver - TeleportPro, Site Sucker, etc. As backup just for sure.
3. Create new WP, setup SEO, GA, silo structure. Do this on internal server.
4. Creating pages with "nice" URLs, make 301 redirects from old pages to new one in .htaccess
5. Copy-paste content from saved site to WP, make titles, meta description and SEO images (alt, title, etc).
6. Create internal links between page again. Make onpage SEO for pages and links.
7. Trash Joomla.
8. Move WP from internal server to public one. Copy .htaccess redirects too.
9. Check for errors, check web log files for erros, etc.
10. That's all!

Timeframe for this will be few days (up to 6 if you process 10 pages in single day). Almost same time you will lost with migration from 1.5 to 3.X. But i will suggest you to migrate to WP because there process for migration is almost one click compared to Joomla. I don't know why Joomla didn't make easy process for updating their customers to new versions... and i was few times upset with that.