How do update the backwards compatibility on my Xbox 360?

Basically I updated my Xbox 360 with the most recent update( which i did via a disk) and I don't have any backwards compatibility. I have recently purchased The Official Xbox Magazine and I have a disk with it which has an update for my Xbox on it which...

I bought an original xbox game to be played on an xbox 360 console. (for the record, the xbox360 console is a friend's, and the game i bought for them is: metal gear solid 2:substance)..the friend doesnt know I bought this game for them, as it is a gift...

A while ago I bought my dad a second hand Xbox 360 which seemed to work fine. Recently he tried to connect to Xbox live but he got an update which he accepted but it got 80-90% of the way and just stopped (constant spinning circle) on applying update...

i have an xbox 360. i just hooked it up to the internet and it said i needed an update, fine by me! so i updated it and it restarted etc. then it said i don't "have enough memory for advanced features." i thought this was ok, then went i went...

Yea i know the question is difficult...but wat i mean is how the xbox 360 starts..im getting the old 360..i know i should get the new one but..i cant..so do i need the kinect to get the new xbox 360 start up.

I want to patch my NBA 2k12. When i go online, the dashboard tells me that the Xbox needs an update to continue. Is it safe to update my Xbox 360? btw, my xbox is modded.