HDV is mpeg2 but not the right flavour for DVD which needs standard def mpeg2. Compressor is a program and yes it is needed to convert your HDV to the correct mpeg2 for a DVD.
The canvas/viewer in FCP is not a reference for color, contrast or resolution. Set to 100% it is more accurate but never for color balanceIf you are actually getting a change in color between FCP and your quicktime, I would be surprised. Try dropping the QT back into an FCP timeline. Do you have a reason to deinterlace, as it will throw away resolution.
Ultimately you need an external monitor to accurately assess your footage.