Domain and Hosting affect to SEO website ?

You're talking about two different categories here like they were the same thing. Google considers some TLDs geo-targetable, and others not. And the explanation is really so simple and obvious that they don't need to spell it out.

History. Wasn't this something you claimed that you know?

There's the common TLDs that have been used all around without any consideration for years before this search stuff even began to be important. And then there's a bunch of newer ones that typically are from some godforsaken island nation that sold their TLD to a company, and that practically ceased to be a country TLD.

Google's own use of domains is a way for them to separate their search in a way that makes sense for their users. It's got almost nothing to do with this discussion.

Google is wrong on some poorly specified stuff just because? You've got to do better than that.

No, I'm claiming the opposite. The TLD they chose does affect geo-targeting of the site! And Google cares enough to put out a list like the one I linked.

Also, it makes a lot of sense for someone like Amazon to choose country extensions because people already know them, and because they want to run separate shops (for several reasons that are not relevant to the discussion). They don't need Google's geo-targeting as a reason, and it probably wasn't working like this when they first opened a shop abroad.

Maybe, maybe not. I happen to come from a country that has very distinctive language, so Google is able to detect it even if you mess up everything on your site. Makes server location much less important, you know...

But as you can read from my previous comment the location of the server is something I would look into. I'm hosting my site in Finland partly for this reason, and have even got IPs in that are registered to the right country from a multinational host that I'm using (just love that service idea).

You can safely tone down the hyperbole. I'm not claiming that this is bogus.

(Some of the more important considerations: for my customers to get service in the local language, and for me to get my invoices the way I want. Electronically, directly to my ERP.)

In my opinion the very first would be making sure that Google knows what country you're trying to target (Webmaster Tools), making sure the language codes of your site are correct (if applicable), and making sure you mention the country (if applicable).

Of course the large and geographically diverse english-speaking part of the world makes language a factor that's quite hard to use efficiently.

Not something I've said. Are you replying to an argument that just exist in your head?