Someone told me that when we are burning a cd/dvd, we should close all other programs(like mp3, video players). If there are some programs running in the background, the cd/dvd created by burning will be of low quality and some data loss may occur during burning. Is this true?

Yes,but to some extent.

I need a free download of dvd burning software that isn’t going to leave a watermark on the picture after I burn it. IT HAS TO BE COMPATIBLE WITH A MAC. I have Leopard.

You can try this dvd burner for mac.
http://www.macdvdconverter.com/mac-dvd-creator.html
Step by step guide:
http://www.macdvdconverter.com/guides/mac-dvd-creator-guide-iskysoft.html
Also, you can search some other software:
http://www.ask.com

I only have a CD burner on our computer, and I really need to burn a movie onto a DVD. How do i download a safe program for my computer (and not too expensive?)? Thanks!

You can choose DeepBurner. Get here:
http://softcluster.net/business/cddvd-tools/deepburner-190228/

Its not expensive..
Its FREE!!