Once connected, you preview what you want to record through the TV. Then when you know what you want to record, you hit the record button and enjoy the show. Then after you're done, hit the stop button, your file will be saved to whatever storage device you use. You will be able record to either a memory card, USB device (PSP, iPod, external hard drive, etc.) or PC (network required).

Absolutely, once in the digital format, video can be edited and even changed to a different format like MPEG2 (this step requires a PC). Once in the MPEG2 format files can be burned on a DVD. Note that saving a file on a hard drive make it easier to manipulate and access the content than if it was stored on a DVD.