If you're talking about single player replays, you've got to know what every one of your joints does in order to keep balance
For example, if you're tipping over to the right, you might consider bending your lumbar to the left, raising your left arm or lowering your right arm and vice versa for the left
If you're falling forward or backwards your ankles become very useful to help keep your balance
There's no method I can give you that works in all cases, you'll have to learn how to work your joints together in order to keep balance.
Punching is a little more complicated than kicking because you usually can't generate as much force as with your legs. In general, you have to use your entire torso (Chest, pecs, lumbar) As well as your hips and glutes in order to set up a strong punch. Your wrists then become extremely helpful because they give you that extra bit of speed you need
If you're going for a punch that will dismember, you generally want to get a bit of momentum going first through an opener which would get you spinning around or something
Feel free to shoot me a PM if you'd like more personalised tips based on, say, your current replays