For No. 1, I think the key thing is that the various parts aren't being seen by the dynamics system because you don't have a connector sticking peg1 to the wheel. Because of that, the first hinge connector isn't following the peg. So I think you have to give the peg it's own dynamics tag and then use a fixed connector to pin it to the wheel. For best results I think you also should convert the primitives to polygon objects so you can use point selections to establish the connecting points.
As you can see, I added some Hair/spline dynamics to fake a string look, but unfortunately that doesn't play with the regular dynamics system. You may be able to use soft dynamics for that, but I suspect it would be quite tricky.