I've noticed that when I split an event, the video and voice start to move independently of each other, which causes editing problems when I want them to move in unison. I do I get these events to move together?
This shouldn’t be happening. Make sure you don’t have the “Ignore Event Grouping” button selected. It’s the one to the right of “Ripple Edit” and should be in the out (deselected) position. You can always group them again by selecting them and pressing “G” as discdude suggests but splitting an event should keep the video and audio together.