Welcome to the forum.
You are currently at the bottom of a steep learning curve.
There is a lot to find out about when it comes to video editing on a PC.
Firstly and generally, the Windows tools are limited and not considered much use for this sort of task so I suggest you look to other solutions.
Secondly there are a great many media players you can try. But have a look at VLC Media player which is open source and will reputedly 'play anything' See
here.
For editing software have a look at
this list.
Also see
this comparison chart.
Software that users have generally recommended on this forum include:
Premiere Elements, Videoredo, Womble Video Editor, AVS Video Editor.
A number of these will have sites where you can download the software to try it.
Some general guidance: All DVD Video is in MPEG2 format. It is a less than ideal media form for editing because it lacks a complete frame structure.
In editors it is generally better to target Inf. files rather than VOB's as these contain metadata about the video in the associated VOB's.
As a result you will be less likely to suffer from Audio/ video sync issues.
You also need to have a good browse through the
Videohelp website which is packed with help and guidance through the issues you face.
See the 'How to' Guides especially.
Good luck.