OK, I'll try to answer some of your questions:
1) Linear and Non Linear Simulation
They say linear simulators analyze ckts in frequency domain without application of any drive level (biasing or applying voltages). What does this statement mean ?
In frequency domain analyses (ac analyses) the circuit is automatically linearized around the operating point, which is determined by dc bias conditions. That is exactly the same you are doing if you apply the classical small signal ac calculations (for example, using 1/wC as capacitive impedance, ...)
2) Secondly, Is non linear simulation (the one finds voltages and current at nodes) same as harmonic balance ?
Each time domain simulation that calculates node voltages and currents as a function of time considers any non-linearities of the circuit.
3)Thirdly, what is the meaning of
Linearized Harmonic Balance
That is a special approach based on the fundamental frequency only and, thus, allows ac analyses also for non-linear circuits.
Transient Simulation
Time domain Simulators
See 2) above
APLAC HSPICE
Simulation packages (programs)
SPICE
A simulation algorithm (kernel) that is used in many commercial simulation programs
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Regards
LvW