Two techniques come to mind. The first is indeed to separate the animation for lower and upper body. Q3 uses such a technique. To improve the quality, you can use some animation blending technique to overlay animations. But this technique has the disadvantage, that it is really hard to get it look right, especially when you want to animate melee combat. For melee combat you often need to animate the whole body to look good (shooters are simpler here).
For high quality animation you should use individual animations for each thinkable movement/action combintation. This way looks best, then you need some kind of FSM or transition graph to choose the right animation depending on the action your character want to do. This is often tighly coupled with the AI and gamelogic and often you will encounter artifacts, e.g. you want to execute an other action, but you need to wait until the animation is finished.
But this technique has the disadvantage, that it is really hard to get it look right, especially when you want to animate melee combat. For melee combat you often need to animate the whole body to look good (shooters are simpler here).
There is a way to make some "half" animations and some "entire" animations? That could make everything simpler
Yes. Game engines usually call this animation blending, though you may see some variant. Most of the higher quality engines support it, including panda3d, the udk, Unity3d, and Ogre3d. Irrlicht doesn't support it properly, though it supports simple transition animations.
When you are coding the animations like this, you generally have access to "weights." For example, if you want to walk and wave at the same time, you would attempt to put the walk and the wave at 50% for both. What happens is that for all the bones it does the walk, but for the arm that does the waving it is suddenly doing the wave, overring the walk. You could also combine a walk and run, which depending on the animation could give a sort of limp, or maybe zombie walk.
