What is the weight limit for this piece? We have a large shade and the chain keeps slipping to the point where I can no longer open the shade.

Don't know a specific weight limit, but we have a vinyl shade for a 42" x 96" window and we ordered this because the clutch wore out after ten plus years of use.

What bead mm size does this take?

Not sure of the mm size. Search”ball bead #10”.

how do you install the side with the pull rope?

Assuming you bought the correct size, the male end should easily fit into the roller tube. Getting the pull chain to line up correctly with your stops, is a bit of trial and error. Separate the chain at the link which joins the two ends. Before placing the clutch into the tube, Thread one end into the clutch one ball at a time until it is completely around the clutch. From here it's trial and error depending on where the stop is located. Connect the two ends and place clutch in tube. Hang the rod and test the open and close to be sure the connector does not stop the advancement before the stop.