Proper convention for schematic component pin input/output arrows
No your assumptions are not correct. Inputs and outputs are generally reserved for ICs. An input has the arrow pointing into the component. An output has the arrow pointing out of the component. Power and ground pins of ICs should be set to "Power". Generally arrows should not be used on connectors. Connectors are passive, so select "Passive" as the pin type for all of the pins on the connector.