"the longer time used to simulate the resonator, the more time points will be used in computing the DFT, which means that the frequency points are closer to each other"

More time points do no mean more frequency points! this is because, users specify the spacing of the frequency samples in the DFT. eg, you predefine the total number of frequency points in the frequency-domain monitor. It does not related the length of the simulation time.

However, more frequency points (sampling) do not mean the narrow resonance can be resolved. The resonance resolution, eg, the full-width-half-max of the resonance is related to the actual length of the simulation time. If the original signal is not long enough, padding error will not increase the actual resolution.

"whether there is a simple relation between the total simulation time and the minimum possible spacing of adjacent frequency points from the DFT" I believe I have replied you:

1: The spectral resolution is inversely proportional to the simulation time in this case.

2: The delta_f is inversely proportional to the signal length in time.

Which is a more theoretical question other than simulation question.