Your example data translates to this:
Q: In the mooshimeter how is the time reffenced?
A: As a epoch or unix time stamp. From the first logged line in your example “1538703591”. In short is the number of seconds that have elapsed since January 1, 1970 (midnight UTC/GMT). You can decode it directly here > https://www.epochconverter.com
Q: Is the time adjustable or able to be zero-ed or is it zero-ed at each log event?
A: No. The number of seconds from 1970-01-01 00:00:00 isn’t retractable. But you can always count the first logget sample as “point zero” in time and work from there.
Q: Is there a date and time stamp in the log?
A: Yes. First and last time stamp.
Q: Can you start a data logging event on a day in a electrical box and leave it there recording for days and collect it later to upload and view?
Q: How is a logging event started and stopped?
A: By connecting the meter to a smartphone/tablet and start the logging- and later, reconnecting it and stop the logging. The smartphone/tablet does not have to be connected during the logging.
To see the data in “standard time”, with a “human readable” format, you can convert the data in (for example) MS-Excel, or write some kind of script like the one i’m pointing to at the beginning of this answer; where i simply upload the log files- or copy/paste the data into a text-field.