What are the limits & capabilities of Op Amps with AC signals?
Maximum frequency than can be amplified depends on which op-amp you bought. Some go to few kHz, some go to few hundred MHz. They all have some frequency limit and they work up to that limit, listed in datasheet as gain bandwidth product. So the limit depends on how much you amplify.

Neither. It amplifies the actual whole signal waveform. You can't just amplify the peak ot RMS, as they are defined by the signal waveform.

Yes, if you made the op-amp circuit in such a way that it amplifies negative voltages to even more negative voltages.