Basically, i want to why when you use a PCB for an RF circuit that the other side of the PCB needs to be a ground plane?
All wires have inductance, even the tracks on a circuit board.
The higher the frequency, the greater effect this stray inductance will have on the circuit.
By using one side of the circuit board as the "ground plane" you create a low impedance connection between the various ground connection of the circuit.
Also, does it matter if the ground plane is broken by tracks connecting components.
A lot depends what you mean by "broken".
If you have just short lengths of track which are surrounded by the ground plane that may be OK, but if the ground plane is divided into "islands" you are back to square one with high impedance paths between the various grounds in the circuit.
Also, if anyone knows why for low frequencies you don't need to impedance match and you can get away with using a short length of wire
Not sure where you are going with this question.
How low is "low frequency"?
Impedance matching can be important at any frequency.
When the length of a wire is a significant fraction of the wavelength at the operating frequency, the voltage measured at points along the wire will vary.
This is due to reflections from the far end of the wire returning to the source and creating standing waves along the wire.
If the wire is a coax cable or some other transmission line, the cable will have a charateristic impedance, sometimes referred to as the surge impedance.
50 or 75 ohms is a common characteristic impedance for coax cables.
If we have a 1 metre length of 50ohm, this represents a full wavelength at 300Mhz.
If we connect the cable to a signal generator set to 300Mhz and measure the voltage at various points along the cable (yes I know that is difficult with coax!), we will see that the voltage varies as we move along the cable, at the open circuited end of the cable there will be maximum voltage, and a quarter wavelength along the cable toward the generator the voltage will be zero, rising to the maximum value again as we move a quarter wavelength nearer to the generator.
This is a rather long and involved subject, if you want to know more, try googling "Voltage Standing Wave Ratio".
Other interesting things happen when pulses are sent along a line, try googling "Time Domain Refectometer"
Does any of this help?
JimB