1. Does my PS2 or Xbox have to be "modded" to play burned games?
PS2, no. Xbox, yes.
PS2: You can use a range of different 'Swap-discs' if you do not want to physically add a modchip. Somebody else with greater knowledge on the subject should be able to fill you in there.
Xbox: Xbox's come with one of three DVD drives, IIRC only one fo them could read burned discs. So you would have to have it modded, and the right DVD drive to read burned discs. Most people download the images and stick them on the Xbox's hard drive to play them. BTW, you can't rip Xbox games with a PC.
2. What exactly is "modding"?
In this sense, adding a third party device that eliminates copy protection on consoles and usually adds a range of other features.
3. Is there a process to make a copy of my discs without "modding" my system?
Only with PS2 and Gamecube. PS2, see above. Gamecube, you probably would not want to bother.
4. For PS1, PS2, and Xbox games, does it matter between CD and DVD blanks? I did my PS1 games on CD.
Well, if the games were originally on CDs, burn them to CDs. If the game was a DVD, burn it to a DVD. Though it is possible to burn DVD games to CDs. I don't know about CD > DVD.
