Is it illegal or unethical to use plotting and graphics styles that mimic those from newspapers and websites?
It's fine to base your graphical style on that of other publications that you think are doing a good job.  There are no ethical issues with this, provided you are not actually reusing images—or parts of images—from other sources.  (For example, you cannot copy parts directly from other figures without either proper attribution or permission; what precisely you need depends on the context and the use you are going to make of the images.  You might also run into issues if you directly copied The Economist's proprietary house font, which was specifically designed for that publication.)