I'm not sure how your changing engine speed with foot switch, trying to figure that out myself. My best guess is engine governor control is somehow connected to the dump valve circuit, the red wire connected to steer switch.
As for the foot switch operation, there are two switches inside the foot switch housing. Each switch has three terminals and they are described using terminology that is common when describing electrical switchs, relays, contacts, etc. One terminal is called C (Common), the other two are called N O (Normally Open), and N C (Normally Closed). The term Normal is used to described any switch, relay, or contact when it's not activated, such as when the engine is off and machine is not in use. All schematics are drawn in the "machine off" position. In the case with the foot switch, Normal would be when the switch is not depressed. The Common terminal of a switch or relay connects to either the N O, or N C terminals of the switch/relay depending on whether they are being activated or not. The N O and N C terminals never connect with each other. In the case with the foot switch, you can see on the diagram the orange wire sends power to the first switch at the C terminal of that switch. So with foot switch in Normal position (not being activated/depressed) the power at C terminal would be connect to the N C terminal being it's the close circuit. The N O is the open circuit in this position. The blue wire for the engine starter circuit is connected to the N C terminal, so in this position, you can start engine. At the same time, the red wire is connected to the N O terminal, this is the circuit for powering up controls at platform. Since it's on the open circuit in this position, there's no way you can operate machine functions while cranking engine. Once you have machine running and are going to operate it, you step on foot switch. Now things are not in there "Normal" position, which means things reverse. The N C is now the open circuit, and N O is the closed circuit. Now, with foot switch depressed, the red wire has power on it to enable platform controls, and the blue wire has no power, so starter will not operate. You have to study it for a minute, but you'll figure out the jumper wires to the second switch. The second switch is connected to the ground (earth) terminal on C of the switch. The function of the second switch is simply to remove residual power from the starting and control circuits after you have used them. For example; your foot is not on foot switch. You crank engine with the power from blue wire. Once engine starts, there could be (theoretically) some residual voltage on the blue wire. When you step on foot switch to operate machine, this action connnects the blue wire circuit to ground (earth), draining any residual voltage left in that circuit effectively disabling it. Same thing happens with the yellow jumper. It removes residual voltage from the operating circuit while cranking engine by connecting operating circuit to ground.