New to CH and STRUGGLING. Arms and Sets/props for CH

I made a tutorial video about them before.
It's in Japanese, but I think it will be helpful.

Case 1
https://youtu.be/yCKxTdkqxys

Case 2
https://youtu.be/dgKTC9bpSM8

You can also download the Character Animator project files by following the links in the overview column.

There are a few things here to respond to (!), so I would take this reply as a source of inspiration rather than a straight solution.

• Separate bits of artwork have been talked about in the forums before (and some people have got it to work). Its not quite as nice as you might think though - you still have to get the arwork right so moving one around in front of the other always gets a black outline correct. You can practice with real bits of paper cut out with a black outline on the edge. One needs to be in front of the other. (If there is no black outline, its much easier.)
• One approach to keep one arm but get less mess near the elbow is to split the arm artwork into upper and lower arm groups. If you cut the artwork just right, what it will do is have one outline in front of the other artwork. I don't think you will be happy with it from your description. So on to the next approach!
• To cut an arm into multiple segments, the easiest approach has been to nest them. By default, meshes (independent layer groups) can only attach to PARENT meshes. This means the forearm artwork needs to be nested INSIDE the upper arm artwork as a separate group, then marked independent. If you do this, you can attach the two layers at the elbow. You will need to put a dragger on the elbow however - putting a dragger on the wrist will only move the lower arm (not the upper arm) - because the lower arm is "independent" it won't affect the parent upper arm.
• With the new Body Tracking support, this is not as bad as it sounds if you use body tracking to move the elbow and wrist. Just tag them both, and the body tracking webcam support will control the elbow and wrist for you. (But that, you had to keyframe / record both the wrist AND elbow, which worked, but was annoying.)
• There is a Leader behavior now in CH which I have not tried for arm joints yet. With the behavior you can attach two independent objects so one follows the other (like "re-parenting" in other engines). I have not tried that on arms. Note that I think one point on one layer will follow the other one (not like a rope joining two things equally), so I am not sure this will work. But could be interesting....

On to figure 2 and the desk (I noticed you "liked" another post recently for this too).

• Furniture is a puppet - a very simple one, but its a puppet too. Background images are puppets too. 
• A puppet cannot be in front of and behind another puppet at the same time.
• That is why the trick of basically considering the desk like "pants" for the character. You put the desk inside the artwork so the arms can be in front.
• There are tricks (like the other thread) - e.g. have a separate puppet for walking around the scene, and another puppet when sitting at the desk. Use cameras and cuts to avoid seeing the character sitting down half way between the two states. (E.g. zoom in on the face, then zoom back out again.) The switch puppets during the transition so the viewer does not notice.
• If you put the desk inside the character, you can try making it independent and marked as "free". I think "free" will mean it won't move with the character (but not sure) - sorry, its been a while since I have played with "free". You might need to put a dragger on the desk, then record a one frame drag for the desk to lock it down to stop it moving. Drag recordings are absolute to the scene, not relative to the character.

Sorry, I have not tried all the above to see which works - a bit busy at the moment. But hopefully it might inspire some experiments of your own.