Your feet are too far apart; you would do yourself a big favor if you slid your right foot up a good six inches, so it is under your right shoulder. Also, you would be better off with your right foot pointed towards your opponent, to the front. The only time it should end up pointing to the side like that is when you throw a left hook.
When you jab, you are rocking your weight onto your left foot, and you do not want to do that. The jab should not affect the weight on your feet, so you can move in any direction while you jab. You throw your right hand like a jab, because you do not rotate your hips and shoulders through the punch. You really need to get turned on the right hand. And the left hook, and here you will notice a difference if you get your right foot where it should be. You'll be able to get your weight turned all the way through and whip that punch.
When you throw an uppercut...The punch starts by rotating your upperbody, and thus your body weight over the leg you intend to punch from. For example, to throw a left uppercut, rotate forward and to the left, until your left elbow touches your left hip. Then you rotate your hips to get your weight back on the right foot, and this drives the punch. It works the same going the other way.
One last thing...When you slide your right foot forward, also slide it to the right a couple inches, broaden your base. There were a couple spots where you wobbled a bit, and that move will fix that.