No, It will not save game memory.
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of coarse this person has no idea what hes talking about, xbox 360 got rid of the proprietary memory cards with the slim, you must have a usb flash drive or hard drive to use your gamertag on the go
They will not work on the old Xbox. But if you have a hard drive on your Xbox 360, you can play old Xbox games right on your Xbox 360, and then you can use the Xbox 360 controller to play old Xbox games.
You Can Use USB Hard-Drives But They Wont Be Able To Do The Same Features As The Official Xbox 360 Hard-Drive And You Will Only Be Able To Use 16GB Of Memory.
An Xbox 360 does not really use a "memory card". It uses a hard drive which is located on the top if your Xbox is in a standing position or on the left side if you have your Xbox on its side. Although you can plug in flash drives or anything with a USB plug-in into the slots located on the bottom in the standing position and the front side to the far left in its position on the side.
You can not play xbox 360 games on an original xbox, however you can play some original xbox games on an xbox 360 console.