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I have had good results by using the rel="canonical" tag on the satellite pages.  If you have access to the satellite pages then copy the content onto the new domain.  Place the canonical tag pointing to the page on the new domain.  I have also found that this will give the new domain a huge boost in initial rankings.

If the content in the subdomains is directly related to the main domain's content, then yes the folder approach would be best. You would consolidate all your links and domain authority into one strong domain. With the subdomain approach your DA is divided. If you proceed with this change, be sure to properly 301 redirect the URLs and update all links within your site along with any other links you have control over in other locations.

Why you consider we should redirect to the homepage instead of the folder of the specific language? "301 redirect each existing site's home page to the new home page for the given language on the efutgol.com site" To clarify, if equipamentsfootball.com is your current French homepage, and www.efutgol.com/fr is the new French homepage, then I am suggesting you 301 from equipamentsfootball.com to the /fr page. In all instances you want to make this change as smooth and seamless as possible for users. This process also has the benefit of retaining the maximum amount of your current link value.

Ok, Here is the keyword  "diseño web vigo" in www.google.es Today it seems like we are in the number one. But it would be something new, we usually rank 3 or 4 for that keyword Thanks

What you are referring to is link triangles. It's black hat, and punishable. You clearly want to perform a link exchange, but you know the links would be discounted. In order to manipulate the system, you link to another site to avoid the link exchange. The bottom line, it is a search engine's job to determine which web pages are the most relevant and reliable for a user. Links are a large part of their calculations. Anything you do to muddy the waters and make it difficult to determine whether a link occurs naturally, or it is paid for / exchanged, it black hat and would be subject to consequences upon discovery.

Rel Author is not for developers.  It's for the author of the content.