What I want to do is to fill a polygon (country) with a graphic file in any format (jpg., bmp., png.). It should look like this:
I'm aware that GIS soft is not proper for such a operations but maybe is there any option to do it only in QGIS.
Use the "raster image fill" style on the polygon layer. This fill style allows drawing a polygon using a PNG/JPG/BMP/... etc.