I'm hoping to get responses back from everyone.

Why didn't you use the conventional topology with a switched capacitor DAC?

Currently I am a student so I choose simple circuit knowledge to understand the circuit well. This is a simple SAR ADC circuit architecture with more components.

I'm used to simulate only small analog circuit, as references and amplifiers. In your case, ngspice doesn't have a simple function to calculate the ADC linearity. You have to output the transient simulation results to a text file, and then make your measurements using another software. It could be octave, or even python. Just be sure you have your testbenches working fine. If you're sure your circuit already works for a ramp or sinewave circuit, then, show us your testbench and simulation control structures.