Are there cases where we do not reverse stitch when sewing?
To understand when to use backstitching, you need to understand the purpose of it in the first place. It's not just "a thing that is done," it is a technique to "lock" the stitches in place on a seam. To illustrate this for yourself, get some scrap fabric and stitch two pieces of it together along a straight edge. Backstitch at one end, and just stitch off the edge on the other, trim the threads, then attempt to pull the fabric apart at the seam on both ends. You'll see that the end you didn't backstitch will pull apart much more easily, while the end that is backstitched will hold more securely.

Cases where one would expect to backstitch the seams are primarily in structural areas; finishing (top) stitching is also frequently backstitched to prevent the stitches from pulling out.

Similarly, you'll need to understand the purpose of the zigzag stitch. In most cases for home sewing, the zigzag is used to help prevent fraying in woven fabrics; because it's not structural, there's minimal benefit to backstitching at either end, though you may find it easier on some fabrics that are more prone to fraying to start on the fabric and backstitch to the edge before going forward in order to help prevent the fabric from being pulled down through the throat plate.

For further information, I would highly recommend taking a beginning sewing course that can be tailored to your knowledge level. Online tutorials and videos are only marginally useful when you don't have the basic experience expected from them.