* How does a home appliance limit the amount of current that flows through it?
Strictly speaking, the way an appliance limits the current flowing through it is usually with a fuse, either a replaceable one or a part of it's circuit board which will melt if too much current passes through it. Electronic devices and appliances are designed to draw only a certain current and if more than that is flowing through it then something has gone wrong.
In normal operation the voltage supplied is more-or-less constant, and so the amount of current drawn for simple devices is based on the resistance of the device. A heater might have two elements, each of which is basically a resistor, if you have one switched on it draws 4A and if you switch both on each draws 4A and so the heater draws 8A. For motors, they have a resistance in their windings and also create a voltage as they spin so the effective voltage is less the faster they go, so the current is highest when they are starting, but the useful power is the current times their generated voltage, so the current is limited either by the load applied to the motor shaft or, if the load is too much for the motor to turn, the resistance in the windings.
* Are there some resistors set up in series in order to cut down the current flow before it actually reaches the device?
Sometimes, but usually the device is created in a way that the work done by the current (power is current times voltage drop) does something useful. 71
For example, a USB power supply will typically be a switched mode power supply, the mains voltage being rectified and then switched to create a high frequency AC which drives a small transformer, and there will be a chip which senses the voltage drawn and regulates how the switch operates to ensure it stays within limits. So if you plug a USB lamp into that power supply, the LEDs in the lamp will draw more current from it, which will cause the voltage to drop slightly, the chip will sense that and increase the drive to the transformer, and because more magnetic flux in the transformer means more current then more current will be drawn from the mains. This can be 90% efficient, but is obviously more complicated than a heater or simple motor.
Two exceptions are some LED indicators on some devices, which do sometimes just use a resistor, and some capacitive dropper LED drivers add a series resistor to prevent large currents if they are switched on at a peak in the AC waveform. In the indicator case it's typically done on high power devices and in comparison is such a small current that it doesn't matter to the overall efficiency of the device - although the indicator itself is only about 1% efficient, if it's indicating whether a the element on an iron is switched on then it is only wasting 0.1% of the total power of the appliance. In the capacitive dropper case the resistor only needs to be high compared to the internal resistance of the capacitor to prevent the capacitor heating up and exploding when you switch the lights on, and once the capacitor is operating normally most of the voltage is dropped across the capacitor and so the power wasted by the resistor is small. 71