Is there an easy way to basically cut out, say, a measure from an entire project and drop it in to a later point in a song without splitting every track individually and moving the rest of the song over?
I've found that regions are usually the easiest way to handle this kind of thing. Make a time selection, do "create region from time selection", and then you can move that region around as necessary.
I use regions for that. Just make selection press "shift-R" and move that region were ever you need it. This way projects tends to quickly get crowded with regions so i make a point of deleting new region as soon as I don't need it any longer.