How does one attach a glass piece to the faceting arm? How large a piece can one reasonably put on there without worrying about it coming loose? Can one put a wider flange or plate on the end of the arm than the one you supply?

The dop for the LapDancer is a standard coupling nut available in any hardware store so you can easily purchase some and have backups on hand. 

We recommend a hardware store 5 minute epoxy for mounting your glass to the dop.

In testing the LapDancer had up to a 3 pound paperweight attached to it and faceted on a larger grinder. 

Since the attachment is a standard screw mount, you can certainly get a larger mount for bigger pieces for the dop. If you work larger pieces we recommend covering the sides of the dop with extra wax or superglue to maintain a good attachment to your glass.