To measure the height of a flagpole. you would use the Meter.
metres and centimetres
I would use a micrometer. A caliper would do as well.
inches or centimieters
Centimeters would be most convenient metric unit for the diameter of a dinner plate.
You should clarify what you want to measure about it: its diameter, mass, weight, color, etc. If you want to measure its diameter, that would usually be specified in microns (= micrometers).
Cubic Meter as it is a solid and that is the norm for volume of a solid
That depends what aspect of a marble you want to measure, for example its diameter, its mass, its density, its color, etc.
Meter.... or more likely millimeters
Calipers would be accurate, a micrometer would probably be most accurate. there's a few options, depends on your purpose.
It depends on whether you want to measure its diameter, circumference, capacity, mass, density, thermal conductivity, temperature, etc.