thank you for your help @songcunzhi but:
My hosts file is totally CLEAR! When I opened my hosts file first time, there wasn't nothing else like it must to be. Even of that, I tried solution with hosts file copy to desktop, save, copy back and replace etc. , also I tried clearing cache with Terminal, also checked my date and time and put my time to automatic adjustement...I tried all from this forum but
my facetime still got ERROR PROCESSING REGISTRATION!
It makes me CRAZY! And It's really ridiculous that one simple program from Apple, program like skype or windows live mesenger, have so many problems with registration!