Studded tires are useful in ice- less so in general winter driving conditions with today's snow tires. I am driving in Maine and it's been decades, I believe since I've used studded snow tires.

I don't think it's necessary to load the trunk with weight. That includes kids, Laszlo!

I can't speak to the LSD question from first-hand experience since I got my ZHP at the end of last winter, but I did install a limited slip as soon as I could. It will be interesting to see how it interacts with the DSC.