"the plural seems to un-natural to fit in the content, or title"

In that case, I wouldn't use it. I can't speak for Portugese, but in English, in the last 2 or more years I can't remember any cases I've had where Google doesn't recognise the difference between plural and non-plural anyway.

What happens when you search for the keyword in plural? Do non-plural results show up? And vice-versa? Trying that out should help.

Even if you search on google.com? Have you tried other countries like google.fr? If google.com is redirecting to the Netherlands' version visiting www.google.com/ncr should stop it.

This works on any localised version of Google (at least those I've tried!). So you can go to google.de and enter Berlin as the location, google.co.uk and enter London etc.

For Facebook your answer is here: https://www.facebook.com/help/131671940241729

You can get some idea of organic image traffic if you use Google Analytics:

Acquisition > All Referrals > click on google and look at /imgres. If you want to see where the traffic is going to (to get an idea of which images) click /imgres and on the Secondary dimension dropdown go to Behaviour > Landing Page.

If it's as simple as redirecting using the same slugs (hence one global redirect rule) then I would redirect the images. If it's complicated then I might not bother, depending on whether image search leads to many visits and conversions to your site or not. Usually image traffic doesn't convert well. If you're migrating to a new domain and keeping the same folder structure it should be as easy as doing one global redirect?

Rather than redirecting I'd most likely take the opportunity to make the filenames of images more friendly than ce7aeffb1e5bdfc8d4288885c52de8e3.jpg by using short descriptive filenames.

Wikipedia editors often delete pages about individuals or businesses if they deem that the individual or business isn't notable enough to have their own page. So in most cases probably not a good idea.

I agree with EGOL.

Another problem with Wikipedia is that you don't have control over the content - anyone can edit a page.

Maybe one day your company will become well-known enough for someone to independently create a Wikipedia page about the company. At that point Wikipedia might be less likely to outrank your own site!

Where possible it's best to group your URLs with pattern matching. If you're only changing the domain name and no other aspect of the URLs you should be able to handle all redirects with one line of code. This is linked in the guide I posted: www.webconfs.com/how-to-redirect-a-webpage.php - scroll down for htaccess (but double check that's the correct formatting for page-to-page redirects).

For when you launch the new website, Google have a change of address tool: 
https://support.google.com/webmasters/answer/83106?hl=en

As mentioned, 301 redirecting the exact old page to the exact same new page is the most important step. Plan ahead and map out your 301 redirects. You want to be sure of what's happening when the domain is transferred to give your rankings and traffic the best chance of remaining intact (or even increasing, which I've seen with some website redesigns).

I think you can change your Twitter handle more than once. If you have a good existing following I'd recommend updating your existing profile to the new handle, and (if possible) re-registering the old Twitter handle at another account - linking in the bio to your new Twitter account. That'll make sure you retain some of the link authority your current Twitter profile has built up and ensure people can still find you through any old links. I think custom Facebook URLs can be changed once.

I actually wrote a site migration guide last week, there should be a few points in there you'll find useful: insideonline.co.uk/website-migration-guide/

Do you still need the old domain? If not you should make the new website reside at www. or non-www.

Imagine telling people your URL "it's at www2.example.com" - most people don't know anything other than www. so it could cause confusion.

Also, if you have the same content residing at the www. and non-www. versions of your website, the two versions will be conisdered duplicate content so you should make sure only one exists.

Adam - remember that PageRank was only updated every few months (these days, even less) - can you be sure if those earlier links were already taken into account before the Wikipedia link was added? Also, maybe followed links came from websites that scrape or otherwise use Wikipedia's content?

I agree that Wikipedia links can be valuable though. It's an edited resource, and it's likely your content will be linked from a page that's relevant to your content, which helps. I've seen decent levels of engaged traffic from Wikipedia links.

If all you do on Wikipedia is add your own links though - you could end up getting banned from it. Rather than just adding links you should be adding value to the page content as a whole - pieces of your research could be really helpful to readers of the Wikipedia page and lead to more traffic to your website. It will also look less suspicious if you add other trusted links and make good contributions to edits on a number of pages. Wikipedia doesn't like biased content either.