Okay the other person is onto the right path but I think it's important to understand the underlying reasons for how "backwards compatibility" works on the Xbox.

The 360 used a PowerPC architecture, which at the time was very cost effective at the time. Pretty much most things now use x86, our standard 32-bit and 64-bit CPUs are this architecture. (ARM is another type that we are seeing now).

Now, you cannot run code from one PC architecture to another, even emulated this is a very costly procedure, every call to the CPU, every call has to be translated. Even with emulation this is difficult. (Note how we're still just now getting 360 emulators).

This is mostly why Microsoft and Sony both said no to backwards compatibility, because there was no simple way to take a disc, pop it in, and play.

So after the massive backlash (which they deserved, but also was understandable their point of view), Microsoft created their backward compatibility program. Essentially what they (or developers, not sure who did it) did, was to literally re-compile each entire game for x86, instead of PowerPC. They would then upload the bits to Microsoft, and that is what you download when playing. The disc you insert is purely for checking that you own it, after that you ignore everything else and download the x86 version which is runnable on your console.

So, it stands that backward compatibility wasn't feasible, it still isn't "backward compatible". They rebuilt everything from the source code to run. A pretty massive effort on Microsoft's part and the developers just so we could play old games. Hopefully you see too why I don't blame Sony for not going through all of that, it's a lot of work.

So to answer your questions:

1. Digitally downloaded in x86 with the disc as key
2. No, it is a simple recompile, from the original source code
3. No, since there is only the PowerPC bits on the disc, there is no way to play the game on a newer x86 cpu without downloading the x86 bits
4. They work the same, once compiled for x86 it works for all x86 processors. (Caveats in software engineering of course, but in this case you can assume they are the same)
5. Microsoft went through a ton of effort to get this working, and developers each had to pull up old projects, figure out how to build them again, and did all of this for free. I'm all for hating on Microsoft for a myriad of reasons, but this was a project that had very little profit for them but did the community a huge service. They have my thanks, and Sony has my understanding for why they didn't do it at the time.