In the top left corner you can see the time and date i want that to change accordingly. And at the bottom where is says "Browser" if you click it, it should open your internet browser. And on the right where it says "Notes" could be like a keylogger or something, lets say you open your browser as an example.
then it will say:
"Browser - opened at Time: 12.34"
On linux it is most likely possible. You'd probably have to make a custom desktop manager, but that would be one hell of a job.
As for win and mac, I never heard of such degree of customization nor of the ability to change the desktop environment, so I'll put my money on no.
Actually I guess you could make a program that dynamically generates the image every time a change is made (best case scenario one per minute) and replaces the current wallpaper with it, and use desktop links with fully transparent icons positioned over text to simulate a button, but it doesn't sound really smart.
I know on Vista there was this thing called desktop widgets, which could be placed on the right of the screen. Some could be downloaded online from the windows website. I guess it might be possible to create your own, but that requires working with the windows API, and most likely in C#. But I'm not even sure if desktop widgets are still a thing.
Mac OS was made with the intention of ultimate stability, simplicity and harmony with hardware. Windows was made with the intention of being usable everywhere by everyone. Linux was made for customization and memory saving.