What 'Admittance' mean in [Bus Fault] option when performing Dynamic simulation?

Well, the fault admittance is always a balanced shunt connected to the bus. This balanced shunt is used to emulate the effect of a three phase fault (very big shunt). A single phase to ground fault is represented with a smaller shunt, defined by the negative and zero sequence impedance at the bus.

I used to represent unbalanced shunts using this fault impedance too. I compute for the negative- and zero-sequence admittance in MVA, connect them in series (for 1LG fault) and put the resulting value as the fault impedance in the positive-sequence dynamic simulation.

Is the shunt reactor connected to the A, B, C phase line of the fault bus separately? I don't know whether the bus fault under this modeling is a three-phase short circuit, a three-phase short circuit grounding, or any other fault.

It is a positive sequence shunt, i.e. connected to all three phases. Only the positive sequence is modelled in PSSE in a dynamic simulation.

This is a three phase to ground fault by default. Other are specified but the worst case fault being three phases to ground. If your system can withstand this type of fault, then you assume it can withstand other, lesser types.