Q2.
Interesting this one, as our FCOM says the same thing, but the 737 maintenance manual contains this statement:
DO NOT OPERATE THE HYDRAULIC SYSTEMS A
AND B ENGINE-DRIVEN PUMPS FOR MORE THAN
TWO MINUTES WITHOUT FUEL IN THE FUEL
TANKS. THE NO 1. (FOR HYDRAULIC SYSTEM A)
AND NO. 2 (FOR HYDRAULIC SYSTEM B) FUEL
TANKS MUST HAVE A MINIMUM OF 250 GALLONS
(1675 POUNDS/760 KG) OF FUEL IN THEM. IF
THERE IS NOT SUFFICIENT FUEL IN THE FUEL
TANKS, THE ENGINE-DRIVEN PUMPS WILL
BECOME TOO HOT. THIS CAN CAUSE DAMAGE
TO THE ENGINE-DRIVEN PUMPS.
I guess the overheat light would be useless on the EDPs, as you can't stop them turning even if they are too hot.