Hi
"I can't figure out how to insert a video clip at the front (the start) of a sequence. Similarly, I can't figure out how to insert a video clip between two other video clips that are already in the sequence"
As well as the method outlined by Borate above. You can try this...
With your clips on the sequence and the one you want to add between them present in the media list, switch into Storyboard mode. Grab the clip/image in the media list and simply drag it down to the join between the clips where you want to place it. (The clips will be shown as thumbnails) . A grey bar will appear as you reach a join. Drop your clip . It will be inserted at the join you have selected..
Nat