You can adjust the length and width of serger stitches. You can either drop the cutting blade or just barely skim the edge to clip any ravels without removing fabric.
If the tension settings are correct there shouldn't be any pulling out of square. I always practice first on scraps. I have a quilt that needed binding, but I couldn't find a fabric that I liked. It has had an exposed serged edge for 8 years and gets washed about 3 times a month.