I'm a beginner in web design and I'm learning through tutorials and I do not understand why the screen width is 1600px and height 616px. Why is not 1920px and whether this is a good solution on the half of the screen?
According to StatCounters Global Stats (gathering data from ~ 2 million websites) currently worldwide about 8% of www users access the web via a 1920 x 1080 monitor.
If you look just at the US and Desktops only, then your question seems more reasonable:
So the real question you face is for whom you are designing: yourself; a putative worldwide audience; the US alone; a specific subset of the US market who all have 1920 x 1080 - most corporate clients will opt for either worldwide audience or at least a broad US market.
Moreover, some older computers not only have smaller lower quality monitors, some have slow load speeds, large network latency and low end graphics cards and CPUs - can you afford to leave out / alienate a wide swatch of potential clients for your client by designing something only a very few will see as intended? Best bet is to use responsive design, use SVG icons wherever possible, set some reasonable breakpoints, and try therefore to design in an inclusive way which will scale based upon the viewer's machine specs.