Is it possible to run something that
looks like an operating system in a web page? Yes,
Eyeos[
^] is one product that seems to do that.
Can you replicate something like the above in C#? Probably, but how to do it is way beyond what the "Quick Answers" section of this site is for.
Could you run an actual operating system in a web page? Possibly, it would be more like a remote desktop into a virtual machine.
Either way, its not something for a novice, and I don't think you are going to find any example code on how to do either approach. There was a site a long time ago that ran an operating system in a web page but I think it was just a terminal command line. I can't find it otherwise I would link it here too.