I would say the answer to all of that is 'yes'. Most people fall into many categories that may be useful for special studies or just making sure we haven't left somebody out. So I would say, add the cemetery category as a minimum, if it is available. If they lived in different places, you can add a category for all of them that were significant. In my family that could mean someone would be in categories for Linn, Missouri (childhood), West Plains, Missouri (retirement/death) and O'Fallon, Missouri (career) and still buried in Arkansas (that's Dad). Dad was born in a JC hospital, but I wouldn't add a category because of that, however, he did later live there while going to school, so that would make it still an appropriate category.
Some counties may be trying to track everyone that appeared on their censuses and you can add those census categories, if categories have been created for them.
But I think even someone like Dick Van Dyke, who was only born here when his vaudeville parents were passing through, would be a person of interest to people working on Missouri notables and would be categorized that way.
In thinking on question 2, it wouldn't be one or the other but both. Again in our family, a lot of people died in a Jefferson City hospital, but they didn't live there, so I would use categories for where they actually lived (Mint Hill, Westphalia, Loose Creek) and not add Jefferson City for that, unless some special project starts wanting to track everyone that was a patient at Charles E. Still Hospital. That doesn't seem very practical, but for some of the veterans homes, sanitoriums and asylums with long term residents, there might be categories for them.
Trying to find someone to use as an example and I notice how much work they still need, but this shows how I have my grandmother, who lived the first third of her life in Ohio and the balance in Missouri, categorized. All subject to change, of course.
I have found the categories very difficult to catch onto myself. Maybe some of that will help.
