Matthews Matthellini End Clamp (Black/Chrome, 2")

Yes, the Matthews Matthellini Clamp with 6" End Jaw (Silver) will easily accommodate a 6" beam.

Not exactly sure... depends on what it is attached to. (i.e. wooden door vs. I-Beam). It's Designed to hold lights so anything around 10-20 lbs. should be ok if on a solid structure.

The Matthews Matthellini Clamp offers a 4 inch wide handle.

This can certainly be used to mount a flash unit to a pole. The clamp will easily support 20lbs(9kg).

You can use it with a grip arm.

I’m not sure what pin you are talking about, but the extenders I am familiar with just clamp onto the end. You may have one of the Matthellini clamps that are configured different. There are about 3 or 4 different Mattellini clamp versions. I have found that sometimes you have to use a short one with an extension to make it work for what I want to do. I have 3 or 4 clamps in different sizes and they are each made different, so many times I try different combinations until I find what works best. They work great and are very solid unlike some clamps that have their use but move regardless of how much you tighten them

These clamps could lock on a bottle when performing a splash shot based on the curvature of the jaws.

Yes, the Matthellini clamp is designed to securely mount onto square as well as round piping.