the minimum distinguishable frequency that a human ear can hear is not an absolute value in hertz but a percentage of the the frequency in question. For example, to go from C to C# in the first octave C0 is ~ 1Hz, in C1 is ~ 2Hz,..., in C8 is 248.91Hz. The percentage difference from C to C# is 5.95% +-0.02%, and this is constant throughout. In tuning my guitar around C4 octave (261.63 - 493.88Hz) I can here ~3 subdivisions from C to C# (I am not that good at it:) so I would estimate that I can distinguish about 2% of the frequency being played.

The search term is JND, just noticeable difference. Yes, the resolution changes over the frequency range, and of course this is true if frequency is given in cents from a reference and even more obvious if given in Hz.

There's much more to read if you find a copy of Brian Moore's Hearing, or Psychoacoustics by Zwicker and Fastl. There is also data about spatial resolution and several other things.

I'm not saying this answers everything but the Fletcher Munson curves give an indication of how our hearing is sensitive to some frequencies and not others. Here is the graph taken from wiki that shows the FM curves and the ISO equal loudness curves for various sound pressure levels: -

A small side-note. As the sound intensity drops our ability to hear bass dramatically reduces and to some extent so does the treble - this is why on older stereo systems there was a "loudness" button - when the volume was low (whatever low means) you could press the button and it would boost the bass and treble a little bit.

It's also worth noting that between 2kHz and 4kHz our ears are very sensitive and capable of "hearing" sound pressure levels significantly below 0dB (20 micro pascals)

Personal experience leads me to believe that a human can detect a 1dB increase or decrease in SPL if they are concentrating.