If I was just answering to your headline, then answer is of course. The OS controls the hardware so definitely it is the only piece of software that is responsible.
If you consider the device drivers as separate from the OS then yes, it can get tricky as to which piece is controlling which resource.
Now to your individual questions.
- Yes.
- Yes, always due to different algorithms of each OS.
- Definitely, due to the differences across OS's and how they allocate resources.
- Technically it's not windows that interacts better with resources, though with various technologies like DirectX, Direct3D, windows allowed device drivers to optimize many calls, hence leading to better performance. This is more of a market issue because windows market is big so device driver writers can put more time and energy into optimizing their hardware. Linux driver support can be somewhat limited. Also the game developers have a larger market in windows, so they are naturally going to put a lot more effort into windows. That doesn't mean windows is a better operating system.
- No. See above answer.
I'm not really sure what documentary evidence you'll need. Existence of lack of existence of some games is a market factor and you can simply confirm that by searching the web for Games by OS.
However I can suggest a bit of reading..
For questions #1 and #2 you may read uo Windows Architecture, an interesting "opinions" discussion Who has faster multi-tasking and finally a summarized write up on different OS's multi tasking v/s single tasking and other details
For question #3 and #4 you might read up on DirectX and Direct 3D and links those lead you do.
"Best" is subjective. Some OSes such as Linux allow configuration for the intended applications, e.g. Server or Desktop (preemptive) kernel, choice of scheduling algorithms, choice of memory allocators. – sawdust – 2014-10-20T00:32:04.170