Is there a relationship between turbojet engine rpm (N1 & N2) and fuel consumption rate? Image Source

N1 and N2 are the rotational speeds of the engine sections expressed as a percentage of a nominal value.

It is similar to the revolutions per minute (RPM) of a piston engine, expressed in percentage instead of in the actual rate of rotation.

They are different because they are characteristic on two-spool engines (see the figure below). The first spool is the low pressure compressor (LP), that is N1 and the second spool is the high pressure compressor (HP), that is N2. The shafts of the engine are not connected and they operate separately.


Image Source
Yes, these need to be roughly proportional for the engine to work, and will move towards an equilibrium if they are not.

The compressor provides the air for the combustion, and injecting more fuel will only generate a little extra power, which however increases the turbine speed, increasing air intake, which will allow more fuel to be burned, again increasing available power and so on.

In practice, if the air/fuel mixture is way off, compressor surges can happen, so in modern systems the engine computer will limit fuel flow.