The bend in my puppet's elbow looks like a problem

Here's some tips for slicing up the arm. Include a little overlap - a half circle should do - on both pieces. Also, change the arm joint settings from "weld" to "hinge." This will allow the pieces to behave like an actual paper puppet.

That one can be hard to get right. Sometimes you can get lucky shortening the sticks in the arms.

The problem is the artwork for the forearm and upper arm are in the same layer, so have the same priority. So it does not know what to draw in front and what to draw behind (and it ends up a mess sometimes).

The most effective solution I have seen is to chop the arm artwork in half near the elbow (maybe have it overlap a bit). (I would keep the original artwork around until you get it right!) Then put the forearm group/layer in front of the upper arms. Because you explicitly put the forearm artwork in front of the upper arm artwork, it knows what should be in front of what. Don't make either layer independent, just chop it into two groups/layers so it knows what should be in front. It can take some experimentation to get the right place to chop it.