You can use your Xbox360 to power the drive. But it's not recommended: for hw safety reasons, banning flags, and just general annoyance.
I seriously doubt you will find a computer that has a power molex already converted to that type of plug. You can buy a connectivity kit for around $20, to power the drive. (I.E. Ck3, Maximus power dongle, etc...)
OR you can/will need to make a converter yourself.
The Via card is for adding Sata (the L shape
) ports to your pc, if you don't have one already. AND
mainly for eliminating compatibility issues between your chipset and the various drives. I recommend getting a Via card as they cost next to nothing and just save people a lot of problems when it comes to flashing, especially with the Lite-on.