Question 1)
See:
http://www.elgato.com/
http://www.miglia.com/
http://www.formac.co.uk/frameset.htm
Question 2) Read the information for those solutions. Many breakout boxes will delay the video so that playing video games through the devices has a response lag.
As for management, right now there are some issues with a third party product called Media Central. I would stick w/ what came with your computer and any software from one of the previously listed companies for your control needs.
I think all those companies/divisions have strong products. It just depends what you want. Cheap is subjective. The EyeTV EZ claims you can use an xbox through it, so that might be a good solution:
http://www.elgato.com/index.php?file=products_eyetvez it is about 150 US though. I believe the elgato software (that would support the EyeTV is updated quite frequently and currently works on a PPC or in Rosetta
"EyeTV had some issues with the Rosetta emulation environment, but now runs smoothly with Intel Macs. Here are the updates for Rosetta. They are PowerPC code, not Universal Binaries, but they work fine on Intel Macs.":
-elgato
I would browse through reviews of software at macupdate or versiontracker for more information.
Good Luck,
-j