Why are some of my sites at top 1# locally (my country) but not listed high at google.com? Think this is strange and how will google rank the site against other locally mirrors? Is it where I get my link from? So if I will rank high at google.fr I should get a backlink from a france site?
This is the problem everyone faces initially, as you say your website ranks well locally but not in Google.com, just continue collecting relevant backlinks for your site, your website will rank well in Google.com as well, just you need to be patient.
Local competition is always less than global. so, if you are looking for global rankings in Google.com, you need to build more quality back links from different SEO sources.
Google knows your personnel preference. They knows your country and search behavior. If you are logged in to the Google account you will see different results than actual results. If you still see the same results even you are not logged in it may due to many resons. -You have many links from local link sources -You have a local domain -etc