You can set the specific encoder by clicking the little reel icon beneath the green + sign. If you want HC, that is where to do it. Or you can set it in the permanent preferences. HC only does video conversion though. It isn't used at all on the audio.
For audio, look under Preferences and select the Encoding tab. The AC3 audio encoder that I have had best luck with is Ffmpeg + Aften.
To correct the audio/video sync on the finished dvd is a bit difficult, but can be done with the correct tools. Unfortunately, the best/easiest to use are not free. I have a program called VideoReDo TV Suite. It can correct audio/video sync problems in your dvd using the QuickStream Fix tool. There is a free, fully functional trial for VideoReDo TV Suite available for download.
I've only used the Quickstream Fix on mpeg2 files. You can reauthor with VideoReDo TV Suite back to dvd-video however.