Ville is correct on all counts but I will try to give quick answers as well:
If so, is the calculation done by post processing logged data, and/or can the meter perform the calculation in real time?
The meter can’t do this in real time, you’d have to log it and do the math in post processing (like excel).
What is the maximum sampling rate for either/both methods?
The maximum sample rate for logging to SD card is in the hundreds of Hz. The meter fills a sample buffer of X samples at the rate Y (where X and Y are the settings you control through the app), then performs math on the buffer (mean for DC analysis, RMS for AC analysis), then writes the result of the calculation to the SD card.
Once the app has started a long term measurement, can the phone be disconnected, with the meter running on it’s own?
Long term logging is done to an SD card on the meter, the phone can be disconnected and the logs retrieved from the SD card later (either over BLE or by physically retrieving the SD card).
Hope this answers your questions, let me know what else comes up, best