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I suggest making sure if that is really your problem.
Fix the minor details, alt tags, remove your meta keywords, fix your sitemap
Dropping to Top 20 doesn't really look like a penalty, more like there are other pages that are better than you.
Take a look at your webmaster tools first for problems and fix those.
Check your keyword average rankings in there and look at your impressions on when you dropped
I also suggest looking your links...its a mix of Russian and sape links
Does feedly count?
Flipboard has been amazing. Been using it since it came out. Creating magazines and getting regular traffic from it.
Im not sure if you can consider scoopt it and paperli with it but they worked fine for me as well.
Triberr is another one.
Good luck Angelos!
Hi Peter
It's possible that they got a link on your site pointing to one of their satellite sites. They hacked those sites/inserted their links and pointed it to you. It's possible that it's an invisible link
Try using your url (the exact page they are pointing to) on google. Look at the cache. You could see it there most of the time.
If not, then it's possible that it has been removed already, through an update of your site or something.
There's no need to have them in the sitemap. If you have them there then its not really a big deal but just try to remove it when you can. If you have a page sitemap, then you can add them in if you wanted to.
is the code showing on the source of the homepage ONLY? or for both?
Take a look at that. You could check the plugin as it also has the ability to assign an author profile to the homepage, like yoast SEO.
you have a bunch of competitors. I could see some doing their own seo. Seems that they've been doing it for a while now. It's normal for it to not rank immediately though.
Basing from your history, you seem to have been hit by a penguin back in october. Maybe you could take a look at your links and check out how you've overoptimised.
I use keyword researcher for that
I dont think that is available at the moment John.
That would be really handy though 
I would start with focusing as much time as possible on fixing the site. Including technical issues and your canonical issues (www redirect, too)
Im not familiar with your internet laws though so I can't recommend any aggressive work. I would just start looking at existing competitors, see what they are doing (use OSE for one) to know what's working for them, and then apply a similar but better strategy. Combine this with other link building strategies and you will be just fine. If they arent doing any seo, then you should see faster results. BTW, since you are new, don't overuse your anchor text ok? Good luck!
Both are good. You cant go wrong with them. It's more of a preference. Ive made both rank so it's not really a problem.
If I was starting from scratch though with no capital (back then free site platforms were very bad) I would go with Google+ and blog there directly lol focusing on G+ now and create the brand there would be what I'd do 
Then I would host some content on a personal blog or wordpress/blogspot.
i would start with your canonical issues
decide also if you want to keep your pagination pages indexed
your meta details need tweaking
you have some www and non www redirect problems
no meta robots
fix your sitemap
image alt tags
and few more
hope that helps
Cyfe, RavenTools are just some that can do that.
I would actually just create a custom dashboard within analytics in this case but there are definitely some tools that can help.
Dasheroo is a new one that I've tried but it doesnt have those yet, eventually it will I believe.
Takeshi hit it right on. You could also look at adding more text (like a caption) that is relevant to the image. Link to it if you have to. Go into photoshop and add metas for the image. Oh, and what works for us in terms of image traffic nowadays are highly popular personalities or brands. They send a lot of traffic, but not that good of a quality
Ive had experienced that multiple times with clients lol
Those are the basic things that id do first, assuming, like what you said, that everything on-page related and technical side are ok.
Share it to both. Get as much eyeballs to see it, basically get enough followers. Force them to +1 it lol. Don't bother yourself with tracking them if each has their own audience
i also run a hundred hotel sites that has that, it doesnt really matter SEO wise. I would test it and look into conversions instead. Good luck!
Hi Matthew
I would look into your backlinks. Since this is penguin, that's the first thing you need to look at.
Having links from sites like these should be one of your main concerns:
The next is your over saturated anchor text usage.
Once you fix those, I would focus on some UX/UI stuff for the site and fixing your canonicals.
Good luck!
Nishadha's suggestion of smushit is a good one so go for that if you are on WP
A CDN would be good for load time but I would still prefer to load it from the same domain.
Try out developers.google.com/speed/pagespeed/insights/ to see more suggestions that you can apply
Hi Graeme
No need to worry about it. Either way, youll get the extra traffic which is a bonus
it's indexed for me. As for the FB page ranking, backlinks. Backlinks in mass works well to rank fb pages. Just dont forget to continue to engage your market.