Main problem may be that depending on the frequency, Your input is on the same order as the input noise voltage. I suggest You simply try it to se if the signal is good enough, its a fairly simple experiment.

You can compensate for the offset in different ways, best method depends on the application. Perhaps adjusting the Ref pin voltage is simplest. 

Yes, it is possible. 2 approaches

Regards

If the signal is digitized, you can cancel the offset subtracting the positive and negative peak to obtain the ac amplitude.  Regards

These parameters are not related to each other.

The minimum input voltage is determined only by the noise level. And there must be at least three times as much.