Firstly am I correct in thinking to convert the to DVD's they first need to be made into MPEG files for TMPEG DVD Author to convert them?
No, not correct. TMPEG DVD Author is only to create a DVD structure. It won't drastically convert your DVD files, you can only convert the audio format in them.
Secondly I have a few pieces of software (Total Video Converter, MainConcept and Cucusoft) and have tried to convert them to MPEG files but the video picture and the audio is out of synch - at some times badly out of synch.
with Total Video Converter I do recommend to use both options while you try to convert, "decode with internal codecs" or "try to decode with DX9..." and remember to convert to DVD format (MPEG > DVD MPEG > NTSC or PAL - what you like)