I want to buy a Canon EF 50 mm f/1.8 II. Does the Canon lens EF 50 mm f/1.8 II work Canon EOS 200D?
I have a very similar camera (Canon EOS 2000D) and a similar lens (EF 50mm f/1.8 STM). Both work fine together. So, the answer to your question is yes, the lens works with your camera.
You should be aware that the EF 50mm on a crop sensor camera like 200D or 2000D corresponds to 1.6 * 50mm = 80mm 35mm-equivalent focal length. Thus, it's a mild telephoto.
In my opinion, it's a very useful lens unless you plan to take pictures indoors in a very small room. The 50mm focal length and f/1.8 aperture allows cool depth of field effects. Not only that, but the Canon 50mm lens is also extremely cheap.
Note that the lens you're considering is the II model, not the STM model. My 2000D camera user's guide warns:
If you use AF with any of the following lenses, using [Quick mode] is recommended. Autofocusing with [FlexiZone - Single] or [Live mode] may take longer or correct focus may not be achieved: EF 50mm f/1.8 II, (some other lenses removed, but the 50mm STM model is not in the list of lenses)
...so the focusing in the live view mode is not as optimal as for the STM model, unless you use the quick mode autofocus (I use the quick mode autofocus all the time even in live view mode). Also, the STM model is better at shooting video, because the focus motor of the II lens is audible and can end up in the audio track of the video.
Also, do note the 50mm lens lacks image stabilization, although at the f/1.8 aperture you probably won't be needing it.