Stop in for a cup of coffee

Not insulated, just sometimes covered. I assume because of the coal dust.

Yes houses with bigger basements would have several rooms. Finishing a basement room is mostly modern thing. Being who I am - doesn't make any sense to me. Basements are not for fine living or fancy finishes. ;)
Yes. In many places much of the food storage would be in the cellar. If you see (or hear) cellar instead of basement - that's the term people used to use for the partially underground storage of 'roots' and fruit, cyder and beer and so forth. In some parts of the early US, it would be seperate from the house. But in the mid-adlantic and north, usually under the house or part of the house. People who lived in apartments and smaller houses in urban areas bought much of the food to cook each day until electric refrigeration became common. It was interesting whenI moved here - some of the older neighbors would talk about the corner grocers as a place their kids would work after school - delivering!

In my old house in Norway there is an oven in the basement. Or "kjeller" as it is called in Norwegian, similar to your old "cellar". We almost never used the heating in the cellar, so it was important to have the floor insulated. Heating was firewood and electricity in the rooms we wanted warm. And the basement was not one of.them.

Bill