Squaring, definitely. If you don't, you might end up with strips that are wonky. They can have a little V at the middle fold, which makes them hard to work with for borders or sashing (they aren't straight). As for cutting vs tearing, I do both. If I'm needing a length of fabric strip, I usually tear it a little wider than I need and then trim the edges. If I'm trying to get rid of extra fabric from backing before I start quilting, I usually just make a notch and tear that across. I find that easier than trying to trim it with scissors or rotary.