Only one voltage, or one current, not a voltage & current pair to calculate power.
Not really. You can monitor continuously, but you’re severely limited by the amount of memory available to you as a buffer to store the values before you need to do something with them. I’m guessing that you’re looking at the inrush current profile to give you additional data that you will use to recognise the appliance. I suspect you’ll need to do some initial processing to minimise the amount of data you store, otherwise it will be very easy to run out of space.
[Edit]
There’s a nice illustration here: How quick is the emonTx V3? - #7 by dBC
I suspect that if you recorded both positive and negative peak values starting when (say) 10% current was detected and continuing until the peak amplitude stabilised, they you’d have a good profile to match to a table somewhere of ones you recorded for comparison purposes. In this case, you’d have about 30 values, which should be do-able.