i own a modded x-box with a xecuter 2.2 pro chip installed..... and heres a way to help you answer some your questions..... http://www.xbox-scene.com go there and you will learn all you want......
NO you cannot play a modded x-box on x-box live (unless it has a off swich!)
NO you cannot play copied games on x-box live (only originals!)
NO x-box chips range from $20-80 on most sites....
YES/NO you can install a mod chip.... (yes if you can solder!!) (if no buy a no-solder mod chip!)
If you cannot get a chip installed just use the 007 game save hack (allows running backups with 007 game & font exploits!) (dont use the exploits if you are gonna use live, it will make you update and patch it!!!)
the easiest way is to buy a pre-mod off sites (range $200-$400 depends if you want a hard drive upgrade to run games off of!)
and if you do use the exploits DO NOT delete or modify the xboxdash.xbe (i did this mistake once) as it will fuck your xbox up!! :)