Running dry can't happen anymore as the pump switch themselves off. Apart from that there is no combustible gas mixture inside the centre tank since the nitrogen generation system fills the center tank with mostly nitrogen, not completely, but oxygen is well below below the required level. Apart from that, yes, center tank pumps have to be switched off manually when the low pressure light (and master caution) comes, not only in the air but on the ground as well of course.
Unmodded airplanes have somewhat different limitations, they should have a placard with those in the field of view of the operating crew inside the flightdeck.
Kinda interesting, the 453kgs limitation is only found in the the cockpit preparation part of our manual, it is not listed in the limitations part.