Let me know if I got your question:
You want to perform screen recording while having a Skype conversation, and then you want to edit this video record by adding short video clips. You also want to burn the project to DVD. Is that correct?
I have some experience in video editing, and given you already got the screen recording program, I can recommend you the following software:
VideoPad:
http://www.nchsoftware.com/videopad/
VSDC Free Video Editor:
http://www.videosoftdev.com/free-video-editor
Both are free, quite intuitive and have what you need. The only thing is VSDC has no Menu option for DVD burning, but as far as I understand, this is not needed in your case.