how to power a SpitzGL-X3000 in a Camper Van

I have a SpitzGL-X3000 and I need to install it in a van. The Power Source ist a LiFePO4 Battery. When the battery is charged to its maximum, the voltage can reach 14.6V.
I guess this does not cause problems, because the power socket on the router says 12V/24V, is this correct? Furthermore, I need to know if the positive lead is the inner conductor of the connector.

Best Regards
Matthias

Yes.

Yes.