Sometimes I hang out with the Pope
I don't know of any specific bells in the Vatican City but I'm sure there must be at least one. Bells also quite literally "hang" from the ceiling.
Other times I spend my time in the country.
Might refer to the phrase "country belle"
I do not have just one correct spelling, but two.
See above: bell/belle
A botanist would describe me as a shape of a plant.
There are a few plants with bell-shaped flowers: bluebells, for instance.
I can be functional, symbolic, or even someone’s name.
Some bells ring, such as Big Ben; some are just decorative, like the Liberty Bell (I believe); Belle can be a woman's name.