For the transducer what is the shallowest acceptable depth from the water line to perform well ? Ie how short can one's pole be?

(queue the pole jokes)

Mine is probably 15-20" under the water and works just fine.

I’m not sure what your setup is. Mine is on a dedicated pole. It doesn’t need very much water. But, it’s kind of like a trolling motor. If you are spot locked on something and it’s rough, your trolling motor could be coming out of the water. I slide mine down to where it’s a foot to a foot and a half down in the water. I can go deeper if it’s windy.

Not sure if that answers your question.

separate pole off bow clear of TM to the right

I set mine about a foot below the surface unless the water is too rough to keep it that shallow.

i think whatever depth you need to shoot across the bottom of your boat in the forward view. I don't have it, but would think even more important if you have the perspective view option. That said, what DaveDave wrote would be the other considerations.