I have a few models of Sony - and most do not have either feature - I have one that has an external mic port next to the hdmi port - but no headphone jack and I think the next higher version of this camera. To get both you would need to jump up a couple of levels.
You would have to convert the video to an appropriate format to be written to a standard DVD. They won't "play" if simply burned to a DVD. There are many freeware applications out there that should be able to do this.