To fix your arm twist problem you have two choices, weight painting or shapekeys with drivers. I am assuming that you are using Rigify with it’s two bone deformation system on the legs and arms. You need to decide if you want to use the stretchy hose feature of the arms and legs to determine which method you use to solve the twisting problem. (Don’t change the constraints)
If you will never use the bone tweaks (this is often the case for realistic humanoids) use the weight painting method. If you want to add some cartoony deformations to your animation, use the shapekey method.
Weight Painting Method:
The two bones system allows you to have two weight maps for deformations . The upper bone will only rotate in the x and z axes. The lower bone is the twist and only rotates in y. It’s nearly impossible to create a weight map that will work for all axes, so the two bone system was invented to solve this by splitting up the deformations.
When weight painting the first bone, treat the second bone as it does not even exist. It should have a strong influence all the way to the end of the second bone.
Your weights should look something like this:
The second bone controls the twisting. The weights should have tapered look.
Notice how the forearm mesh has a smooth twist from the elbow area to the hand. All of the edge loops make a smooth arc. The hand in these images is twisted 90 degrees. This will help weight paint a smooth transition.
Don’t go by the color in these images. These weights are not normalized. I suggest using that option when weight painting to get all values to equal 1.00
The down side of this mothod is you will break the stretchy hose (arm/leg tweaks) of the rig. You need a different weight setup to make that look good.
Weight your bones without extending the influence very far past the bones. It should look more like this:
This will make the tweak bones behave in a way that keeps them useful, but your arm will twist badly like in you images.
To fix the twist, create one or more shapekeys to smooth the twisting. Add drivers to auto correct the bad deformations. I know that I don’t need to give you a tutorial on how that is done as you are the king of drivers. I use the ORG bone positions to drive my shapekeys.
The shapekey method is the longer route, but it gives you better control over the mesh and it will not destroy the tweak bones functionality. If you weight too far past the bones end points (like in method one) it looks very bad when using the tweaks.