This is what we call "Z" turning. Sometimes you get on the new edges in the fall line, but you are basically releasing the old edges, pivoting the skis, then setting the new edges and skidding. Garret has your number, but you called it on yourself first. Yes your hands should come down to belly button height, but don't worry about them for now. Yes you should finish your turns more. This will start you on the road to making C shaped turns instead of Z shaped turns.
Try a drill called carved traverses.From a position standing on one side of a wide trail pointed to the other side, but slightly downhill, check for traffic then traverse across the slope tipping your skis onto their uphill edges. As you build up speed, you should start turning uphill. Go uphill until you stop. If you don't turn your feet to make the skis turn uphill, then you will leave thin tracks in the snow. If you do, you will leave washed out tracks. Don't do that. If you do, then take a shallower line to go slower across the slope. Once you can leave thin tracks, increase your starting angle to go faster and have more of an uphill angle to your finish to a stop. Do this until you can feel the G forces build up. The next step will be to start a new turn before you come to a complete stop. Try it. Then you will be ready for other drills.