You don't need a TV connected unless you want to see when to start and stop recording and maybe edit the content.
You won't be able to copy commercial copyguarded tapes.
should be perfectly possible, but you need a screen to monitor the input / output, otherwise you have no idea that the video is actually being copied over, and if the input is of a decent quality. Also a good idea to monitor the audio levels too!
You don't need a TV connected unless you want to see when to start and stop recording and maybe edit the content.
You won't be able to copy commercial copyguarded tapes.