Tons of problems trying to simulate simple rope without elasticity

[Romahaaa]

Hey,

I spent tons of time trying to simulate the rope I need. 
The idea was pretty simple - the rope must be attached to the pencil, and the paper clip must be attached to the end of the rope. Moving the pencil paper clip had to behave more or less realistic way, but I couldn't reach it playing with all the parameters and iterations. I also checked all the test scenes, and still can't get, why it's so complicated to implement it.
The issues I got:

1. rope and paper clip NEVER stops moving while the pencil is static. Here is the video.
   
2. rope behaves like a fishing string moving the pencil up and down. Furthermore it looks like paperclip has 10kg of mass while it's 0.01 only. Here is the video. 
   I need the rope similar to this      As you understand such type a rope don't stretch at all an don't.
   
3. the worst issue - if I move down the pencil and paperclip collides with a surface, it behaves veeery weird - instead of laying down to the surface it "floats" in the air, and the rope starts to shake as crazy. Here is the video.
   
4. artifacts with attached objects - looks like the attached paper clip (but I also will add more attachments) position doesn't follow the particles position properly. You can see in the video I mentioned in #3 there are some gaps between paperclip pivot point and end of the rope.