Bike stops in place when trying to manual
Yes, that's the effect of your Mass Center moving around a reference point, in this case your bike. You and your bike make a whole thing, So when you "preload" you shift your torso towards the handlebars and down, which makes the bike to go away from you on the oposite direction. Given that you have foward direction, it anulates. And when you pull up your front wheel, your back wheel should be coming under your body. Meanwhile you bend your legs and stretch your arms, counterbalancing the weight of the front portion of your bike. So in short, you try to mantain your balance point(center of mass) over the back axle and near it.

Other thing is that a wheel, or any object that has mass and rotates on an axle. Has a "Moment of inertia(aka rotational inerti or angular mass)", which means the faster the wheel spins, the harder is to take it out of it's trajectory. In simple english, means that it's easier to go straight on a manual the faster you go, because the wheel won't like to lay down with more speed.

To lean either right or left on a manual, you should do it bowing your feets and knees. It depends mostly where you put your weight on your pedals, so leaning your feets both to left will make a sharp turn so be careful.