Could someone explain to me how, during the descent, the pumps pull the oxidizer and propellant? I could be wrong, but during the burn the propellant should move inside an almost empty tank.
Falcon first stages also have cold-gas thrusters at the top of the stage; you can see them firing for thrust perpendicular to the stage during some landings. Among other things these thrusters can be fired downwards (parallel to the stage) to provide thrust for ullage. A few seconds of thrust will settle propellants at the bottom of the tanks immediately prior to engine ignition (this is probably necessary prior to the boostback burn, for example, as the rocket is clear of the vast majority of the atmosphere by then).
During descent, the stage is flying with the rocket nozzle in the flight direction, which means the "bottom" of the tank is also oriented in the flight direction. Since the stage is decelerating due to atmospheric drag (and engine burns) the fuel is "pressed" to the bottom of the tank and can thus be pumped like on ascent.