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Taximes
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Close, but not quite. I'm not sure why you've written down the peak current, especially since you've written I2rms. 5kVA/110V = 45.46V ...?
Presumably, what they want in this case is just the magnitude of the impedance. Since you know the magnitude of V2 and I2, you can then determine the magnitude of Z2.
No no, any and all quoted voltages, currents and powers are always in RMS unless explicitly stated or expected to be otherwise. If you ever stand back and ask, "Hey, is that RMS or something else?", then chances are good that it's RMS.
Peak is quote often a terrible measure to use since it implicitly assumes that the reader has knowledge of the shape of the waveform. For example, in your question above, you assumed that the input was perfectly sinusoidal. However, this is not always the case - even for mains voltages (it wouldn't be unexpected to see a bit of third/five harmonic in the mains chopping off the top of the sine wave so that the peak ends up lower than expected. A consequence of the standard transformer-rectifier-dc capacitor design decision).