OK, don't apologize for your English, which is excellent ;) and, no I didn't understand you at first, as at that moment your background image was fixed and not in full mode. Let's see:
what happens is that the image is typically at 0.66 height/width proportion, equivalent to 600x400 px. The image resizes correctly and shows in full when the browser window's proportions allow it (doesn't matter if it's the actrual screen or just resizing the browser window).
If the window is wider, for example cinematic proportions of most modern screens, the width will resize to keep with the widening window, which means that some part of the image needs to be cut out in order not to deform the picture. This is done by default from the bottom up.
The same thing applies if the windows proportions vary towards a portrait. When height grows more in relation to width, beyond what the pictures original proportions allow, it must either cut somewhere or deform the image. The cut is done from the right in, which is why your iphone cuts the nose ;)
It's the same efffect as in cinemascope films in old television: some countries/channels would show the film in a letterbox format, with black bands above and below in order to show the full image, and others cut left and right in the image, covering the whole screen with image -- but sometimes you got people talking out of the frame ;)
After all this explanation, is there a solution? Well, no, not as such, unless you want a deformed image (a weirdly fat or thin face, depending on the device). Because most screens nowadays are cinematic wide-screen, you could choose a wide-screen image where the important parts are heavy on the left, so that the image degrades somewhat gracefully in 3:4 or portrait mobile things -- just doing a mirror version of your current image, so that the guy looks from the right will help a lot, especially with the iphone
Sorry about the news, but there's no magic, at some point you either have to crop the image or deform it. I guess cropping is the better choice, especially if you choose your image thinking of what will happen changing the window format