Minimum resistance for a home circuit to not have short circuit
It seems that R = V/I = 22 Ohms would be minimum resistance to not break the circuit.


This is correct.


  So if this thinking is correct, any appliance should have at the very least 22 Ohms resistance?


This is an oversimplification. There's much more to circuits than resistors. 

A toaster or an incandescent light bulb might be analyzed this way, since it's basically just a resistor.

And there are some books and engineers who like to define the "resistance" of a circuit as the ratio between its operating point voltage and currents. In which case your thought is correct as a tautology. 

But something like a TV or a computer will have a switching power supply using the mains power to produce an internal DC voltage (or voltages) that actually power the useful circuits. In these circuits don't mainly dissipate power in resistors at all. They use transformers, diodes, capacitors, inductors, and transistors, mainly (resistors are used to adjust control signals, but very little power should be consumed there). This circuit uses feedback to adjust itself to draw the current it needs to provide power to the internal circuits. This actually means it will behave like it has negative differential resistance --- if the mains voltage goes down, the current draw will go up, at least to a point.


  And finally do some small appliances put in extra resistors just to not cause a short circuit?


This should almost never be necessary.