imma answer these for you:
1) games have always been able to run off the HDD via modded console("always" is a loose term), and the rest of this answer i'll follow in the next question.
2) NOW you can, before you COULD NOT. your kernel has to be 17349 or higher. ever since that dash, they removed the special USB limits, and allowed STOCK/Retail units to store games/XBLA/DLC/TU's on a fat32 usb drive.
3) quite possibly if you setup said drive as your system drive, but you would need no internal hdd.(this is a theory, NOT tested)
3.1) someone would need to test a retail unit with this, as like i said, they changed usb stuff, and maybe if you set usb as system drive, and put in an OG game, they might have a different setup for this.. as i stated, all theory and no facts.
havent tried this game, theoretically it could. i know for a fact MTS5 you can not. i tried to test that particular game, and you would need an internal hdd. OFC they could have fixed this "bug" since then, seeing as they are supposed to allow external hdds to be system drives.