The weather data you are describing is based on ATIS/TAF/METAR weather reporting formats.
The format is highly standardised by the ICAO and the WMO but there are international variations; for example, the FAA reporting format for North America departs from the international standards in a few minor ways, mainly related to non-standardised units of measurement, such as atmospheric pressure (measured in mm Hg in the US versus hecto-pascals in Europe and elsewhere). It looks to me that BMS follows the ICAO standard but I’m sure one of BMS veterans will be able to say definitively.
I don’t think there is any information in any of the BMS manuals (if there is, I haven’t found it either), but there are a lot of resources online to help.
Check out this thread https://www.benchmarksims.org/forum/showthread.php?11969-Reading-ATIS-Shorthand&highlight=METAR for assistance.
