I am puzzled about the equivalent circuit of digital IC's input and output ports.
I consider the input port to be an equivalent resistor and equivalent capacitor parallel to the ground , and the output port is a voltage source series resistor
to the output .The voltage source voltage and resistor value depend on the level of the output.
Yep. In a modern ASIC there is still a lot more. You can expect a lot of level shifting going around, a lot of clamps for ESD protection, buffers, etc.