I would personally merge all the character's part to make one object, it would make things easier in my opinion. But first select the armature, display the layer with the deforming bones:
Then shift select the mesh and check the bones, you can see that some have influence when they should not:
Select these parts in Edit mode, in the Properties panel > Object Data > Remove From All Groups, then reassign to the right group (the one that has the name of the bone that is supposed to control) with the Assign button. Or do the corrections with a brush (in Mix or Subtract mode) in Weight Paint mode.
For the smoothness yo could add a Subdivision Surface under your Armature modifier, but you should add edge loops where the bending is happening (by the way, no need for so many horizontal edges in my opinion, especially if you add a Subdivision Surface):