Yes, it is possible to emulate hardware.
Yes, it is possible to emulate hardware.
Yes, a program that mimics hardware is called an emulator. If you want to build one, this gives a clear idea of what it could be like. The code snippet shows memory allocation for a large address space and outlines how instructions might be handled. For more details, refer to the guide on the Gameboy CPU and its instruction set. Enjoy your project!
I believe you can reach what you need by checking these Xbox specifications and using source/template design tools from Qemu and Qemu wikis. You can build a new BIOS or hardware setup with proper mapping—like HDMI to your graphics card, Xbox controller to keyboard/mouse, etc. However, if the system has any DRM or security measures that require specific identification of the Xbox, it will likely still fail.