This bass is a 21" scale, with a piezo saddle mounted in an adjustable bridge. The soundhole is just for looks. The strings are metal-wound Kalas. The fretboard is cut out of the ugliest piece of wood I ever received. For such a small neck, I managed to cut around most of the ugly, and the result isn't half bad.
You can build a guitar with just a jigsaw. It will do everything you need to do, it just won't do it as well as a scroll saw or bandsaw. The biggest problem with a jigsaw is that the blade is only fixed at one end. It stays fairly perpendicular when cutting straight, but will get pretty crooked cutting curves, especially in thick materials. If you are going to use a jigsaw, cut well outside your lines and sand-in.