Well, lets get the the basics of a centrifugal pump out of the way. KSB’s basic pump was a kinetic pump. It included a shaft-driven impeller that rotated inside a casing. Liquid flowed into the suction port (inlet) of the casing and was thrown to the outside of the casing and then exited through a discharge port. The velocity imparted to the liquid by the impeller was converted to pressure energy or "head". In its simplist form it looks something like this:
If you really want to get down into the actual engineering, I would suggest this site: Working of Centrifugal Pumps
While von Braun realised that fire fighting pumps could offer a solution, it was not an off-the-shelf one. He contracted with KSB in 1935 for a pump and KSB had significant problems. They had to deal with extreme temperatures, difficulties lubricating the liquid-oxygen side, especially the bearings. Cavitation due to bubbles in the propellant was so severe that the resultant vibration problems (which lead to explosions) required major interior redesign work. Then there were the seals and gaskets and the need for lightness and compactness (new alloy selections) which also posed fundamental problems that required years to overcome.
As I stated before, not something that was off the shelf.
von Braun pretty much left the development of the pump and turbine to Thiel’s propulsion group and the engineering group at Kummersdorf while he concentrated on the guidance aspects.
The pump, as designed, used a 2 blade row Curtis turbine to move the centrifugal pump for each shaft end. One shaft for the movement of 72kg/s LOX at 23 bar and the other for the movement of 58kg/s 75% ethyl alcohol and 25% water at 18 bar. All of which impacted into the burn chamber at 15 bar.
Here is a cutaway view of the A4 rocket turbine/centrifugal pump unit
From the left, the alcohol pump, the 2 stage turbine and the LOX pump.
Here is a simplified diagram of the assembly
Since you only asked about the “firefighting pump”, I won’t go into Hellmuth Walter’s “steam generator”.
References: “Process Centrifugal Compressors: Basics, Function, Operation, Design”, Klaus H. Lüdtke, page 7.
“The Rocket and the Reich: Peenemunde and the Coming of the Ballistic Missile Era”, Michael J. Neufeld