the stock pump is sufficient unless it's got some high mileage on it, in which case you should perform the major service interval and replace the
-timing belt
-tensioner
-waterpump
-oil pump
as they are all on the same side and in close proximity to one another.
no you dont need to change it, which unit are you buying? MFactory has a nice one
You dont need to change your pumps.
Did you get an adaptor fitting for the sandwich plate? or will you be removing the factory donut cooler and blocking off the coolant ports?
It affects cranking pressures, i.e. takes takes a second or two longer to see full cold start-oil pressure.
Why do you need an oil cooler then?
is your car run on the circuit alot or is its engine highly modified? turbocharged?
That kit is going to over cool your engine oil and cause more problem than good. Go for a good thermostat controlled adaptor, i,e, the one I use is from Mocal , it has a themostat allowing for proper oil temperature.
If the motor is equipped with a stock oil cooler...water to oil exchange unit...just opt for a larger radiator and ensure that the sides and top of the radiator are blocked off so air is diverted directly into the radiator.
An external cooler is not necessary.
Spoon has had success running enduros without ever using an external oil cooler. They just relied on their large capacity radiator and the stock oil cooler.