How can I cover a window in a nice way
You may want to consider just applying some of that opaquing film to the window glass that just goes part way up. You wouldn't get your plant shelf but this would be an easy solution to the people looking in. 

Since you live in an apartment your range of options of that you can do are limited unless this is a unit that you actually own. And even in the case that you do own you would not want to go so far as modifying things in a way that they are not reversible without damage.

One scheme that should work would be to look into using a sheet of the dense pink or blue rigid foam insulating material that is cut to length so that it fits across the window opening with a push-in friction fit. This material comes in large panel sizes (in USA ~4 feet by ~8 feet) so you could achieve the size of covering that you need.

For the shelf it may very well be possible to cut a narrow strip of the same material that fits into the opening and sits flat on the upper edge of the material that covers the window from below. It could bonded or pinned to the lower panel as well. 

To improve the look you can try spray painting the foam to a color that coordinates with your room.

Do note that I am not suggesting that you use the lower cost white crumbly foam panels.