1. In AC analysis, shouldn't both the resistors (RC and RL) be in parallel?
Answer: Yes, correct. This is because - as seen from the output of the current source (BJTs collector) - the ouput current Ic is split between Rc and RL. That means: For gain calculations both resistors are in parallel.
For the cut-off frequency we have to analyze the circuit from the capacitor side (and NOT from the collector side). Simplest method for finding the time constant of an RC combination: Find the current through the connected resistors - when the (charged) capacitor discharges. As we can see - the capacitor discharges through the resistors (left and right from the capacitor).
Thus, we must consider the series combination: Time constant T=C(RL+RC).
2. We don't we consider the RB (input resistance) for cutoff frequency?
Answer: When there is is no (external) coupling capacitance there is no input time constant and no corresponding lower cut-off frequency .
Supplement: Time constant (high-pass cut-off) of the output RC combination shown circuit
From the circuit diagram it is evident (as mentioned already) that the time constant - as derived from the discharging procedd - is T=C(RC+RL). In particular, this is true because the BJT is treated as a (ideal) current source (no current into the collector during discharging of C).
Question: Will we arrive at the same result for the charging process? For this purpose, we have to generate the differential equation for the case that a current source I (input step) is charging the capacitor C.
Curent through RC is ic(t)=Vc/RC (Vc=collector voltage
Current through RC is io(t)=Vo/RL
Current through C is the same: io(t)=C[d(Vc-Vo)/dt]
With Vc and Vo from the first two equations and with I=ic(t)+io(t) we arrive at the equation (dropping the brackets (t) for clarity):
io=C[(d(icRC - ioRL)/dt]=[(d(I-io)RC - ioRL)/dt]
Beause d(I)/dt=0 we can write (after some minor manipulations)
io=-C(RC+RL)d(io)/dt.
Setting (Ansatz) io(t)=Iexp(t/T) the solution of the diff. equation is
io(t)=Iexp(t/T)=-C(RC+RL)(1/T)I[exp(t/T)]
From this: T=C(RC*RL)
Result (Summary): : The time constant T for the output circuitry can be calculated using (a) the discharging or (b) the charging process of the capacitor C.