You can set your resolution to whatever you like that your monitor supports. Your monitor is able to be at 1920x1080 however if the icons are to small or you don't like how it looks you can turn it down to perhaps 1680x1050 or the resolution you presented 1600x900 you can do this all in the screen resolution tab.
My 21.5" Samsung T22B350 allegedly has a native resolution of 1920x1080, however, trying to run it at 1920x1080 makes text appear extremely small, and formatting ratios are very off.
Can I do something, or do I have to run in 1600x900 for all eternity ?
It is a 1920x1080 resolution monitor. And everything looks small because that's how resolution works. The higher the resolution, the more things can be on the screen at a single time, the smaller everything will be. Not sure what you mean by "formatting ratios are off". If you are referring to something like wallpaper, then yes, potentially if you have a wallpaper for a 1920x1200 or 4:3 ratio desktop and you want the wallpaper to fit on the screen from edge to edge without anything being cutoff, then yes the wallpaper will look distorted. That's how aspect ratios work. If you take a square picture and you want it to fit in a larger rectangle from edge to edge guess what is going to happen to the picture?
Yes, you can use lower resolution to increase the size of everything. If 1600x900 makes the text still too small to read, then try 1366x768.