First when I work with other musicians I discovered they gave me tracks that were recorded at a wide range of frames per second. A free piece of software called "Handbreak" will remedy that problem. It can batch process the files and does so very quickly.
The second problem is called "audio drift". That occurs when 2 different devices are used. One device is capturing video and a second device records audio. Even though your camera might say is it recording at 30fps; it in fact is most likely recording at 29.97. Initally things will appear to be in sync but the gradually drift out of sync. Again all of this can be easily fixed in "Handbreak". You then simply reattached your new audio track to the video and everything will be perfect.
This solution will also sort out the issue with a single track & video.
Hope this helps.