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It could also be just a link that should be relative, but is not.

you can use screaming frog SEO spider to find the page that is linked from.

Please consider the user first. A user is confused if he found a page for a wedding magician and on the same page a coporate story.

And keyword wise it is much easier to have 2 different pages for google. If you want to know all in's and out's i would have to write a blog artikel, but just 1 page, 1 message and 1 specific keyword is optimal (do not overdo it)

Ryan is right from a technical view.

But, i would be very hesitant to change the page based on the onpagegrader. My assumption is that google looks at a website and takes the content a customer can see. The fact that the keyword appears in the links seems somewhat high, but you are a into physical therapy! ( the alt text seem varied already)

So unles you have a problem with google i would not focus on that.

Focus on the fact that you should have just 1 H1 Tag ( prefereably not a picture) and the way to long title tag. Fix the / non dash duplicate content problems etc etc..

Well, testing is the best way.

But if you want your video to show up in the serps (which almost never happens anymore) you can limit yourself to 55 characters. (the lenght of the title tag). If you focus on Bing go for 45.

But any other motivation based on your own platform is OK as wel.

If you consider the amount of characters that is read on twitter (the first 45) you could try to limit it to that (be concrete for your customers)

Having content is always nice. Creating great conten takes time and efford. Asking people to make content goes better if you already have some content. So please choose some "valuable" or "evergreen" conten of the old blog and post it on your new one.

Creating 301 redirects from the old domain is a good way to rescue some of the old link value. Even if you do not see it in moz and majestic, it still could be there. It is not to much efford if you know what you are doing. So go for it.

If redirecting each post is to much work redirect all posts to your /blog/ directory. LInk value and visitors will get what they want!

go for it!

Yes! Google would punish you (or do not give you credit for the links) if you would overdo it.

Matt Cutts explained that using pr articles, press releases and blog spinning in order to get more (or to much) links was not allowed and a nofollow should be added to the links.

Also excessive use of linking from widgets can be a reason for penalty. The question is: what is excessive?!

Google is all about unique content. So no excessive content spinning.

Back in 2008 there was "proof" that the anchor text of a second link on a page would not be counted for the anchor text.
In the MOZ starter guide it is still advocated: https://moz.com/learn/seo/anchor-text

BUT in 2014 it was reported on searchengine land:
http://searchengineland.com/googles-matt-cutts-one-page-two-links-page-counted-first-link-192718
That the second link might be counted. Direct link to the matt cuts video from 28 may 2014
https://www.youtube.com/watch?v=5AsLWIuNNMU

(Even in 2010 there where already some different opinions and work arounds.
https://moz.com/blog/the-first-link-counts-rule-and-the-hash-sign
https://moz.com/ugc/3-ways-to-avoid-the-first-link-counts-rule (2011) 

Question: did anyone recently test this recently?

The deeper questions are:
1:is the LINK value counted if you have more that one link on a page to another page?
2: is the Anchor text counted if you have more than one anchortext to another page?

The most interresting i have is that i have a menu from which i link to my important pages. Does it help to put extra links in the content to specific pages?

I have done a test of my own.

I used a very important page on my website.
The page has not been changed for more than 2 months.
The page has a link from the main menu with the money keyword "zoekmachine marketing" 
I used the blogpart of my website to add 5 extra links like this: https://www.stramark.nl/zoekmachine-marketing/#4-p-zoekmachine-marketing

I ran the keyword ranking on the specific anchor text on the 9th of july, and today again.

The result is significantly positive. I will monitor for a few extra days

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Have some international links can always help you out for your authority. Creating some englisch content/resources might be a good idea in order to attrackt links.

Creating your own profile page in englisch is a great place to start. This way your international buddy's can figure out what you are about, and you can link to it with a good reason.