how to record to a dvd that is partially recorded?

Is it that you want to record more data on them? If so, fill up the remaining available space, then finalize. That will be your only solution to this problem.

You can if it was used as an open session and the disk was not closed or finalized. A lot of the time Windows/ Nero will however complain its not blank and refuse to use it. I believe the drive has to support packet writing.