The transducer cable will do just fine around the shaft of the trolling motor. All that loose cable is gonna be trouble if it grabs a limb or something. Ask me how I know.
It's weird. I know I have intermittently in the past, but I also know I didn't this past weekend. I think in my case, it had to do with the proximity of the extra transducer cable to the Junction Box for the TM plug. That's the only thing that could be variable in my setup, and I've certainly never done anything to address the issue specifically. If it is a serious concern for you, a professional install might be worth it for peace of mind.
Either is acceptable and I've seen posts from people who ordered extras and put them on both, as both cables are capable of picking up interference. I chose to install them on my power cable because 1) my old Humminbirds had them built into the power cable, and 2) due to the close proximity of my starting and TM batteries I felt I was more likely to get interference from the power cable.
You are correct, and though I didn't show it here, I did do exactly that! I do however want both transducers installed, because vertical jigging is a big part of the walleye game so the guy in both the front and the back can watch their baits independently. Someday when I cash my billion dollar PowerBall ticket, I'm going to get live scope and I intend to only run one transducer on the Stern to be shared by both units as you described. Thanks for watching and tight lines!