thats a lot of questions mate!
to rip games you need a KREON drive (google this and look for KREON on ebay), or you can take out the 360 drive and hook it up to your pc.
to burn them you need a dual layer DVD burner, a program called IMGburn and Verbatim dual layer DVDs
to patch, check and verify backups you need a tool called ABGX. current version is 1.0
to play backups you need modified firmware on your xbox 360 dvd drive. latest firmware is ixtreme 1.51
if you want to go on xbox live and be absolutely sure that you dont get banned, DONT MODIFY YOUR CONSOLE IN ANY WAY!
a good place to start is search for how to find out which make of DVD drive is in your 360.
you need to just READ READ READ READ before you do anything. takes ages to learn about all the various methods and programs