Is the standard unit for measuring capacity in the metric system?

Answer 1

If you mean capacity as in volume: the basic unit is cubic meters, since lengths are measured in meters. Of course, cubic centimeters, cubic millimeters, or cubic kilometers can be used as well, depending on the application.

If you mean capacitance: the modern version of the metric system, the SI, the basic unit is the Farad. Since in practice this is a very large unit, usually smaller multiples are used, such as microfarad, nanofarad, or picofarad.

Answer

There are just seven base units in the SI system. 'Capacity', in the sense of volume, is measured in cubic metres which is a derived unit, not a base unit.

Answer 2

By capacity, I assume you mean volume. That would be the liter.