Is there any role of Operating system in C++ compilation process

I am new to C++ and I was going through this article : http://ift.tt/2m9usI0

I have few doubts,

• Does Operating System has to anything when the *.o file and *.exe files are created by compiler or is the architecture of compiler(for that OS) that controls whole compilation process.
• Secondly, if I am working on Windows OS with two different CPU architectures(let it be AMD, intel). Now, I create a sample.exe using C++ on machine1 with intel processor. Then I try to execute this sample.exe in machine2 with some other CPU architecture, say AMD. my question is how will same 'sample.exe' file will execute the same instructions on two different CPU architectures.

Sorry for any wrong terminology used, if any.