Why is some of the food on one side of the store, and some of it on the other, with the non-food items between them? Is it in hopes that customers will pass through the non-food aisles and pick something up?

Yup. Search for "supermarket layout psychology" for details :->

Toothpaste and cold remedies, let alone shampoo and batteries, are not usually impulse purchases.

I don't think they're necessarily hoping for impulse purchases for these items, but people might have been thinking they'd pick up those sorts of items at a nearby drug store but then realize they can get them at the supermarket.