Correct, this is the raw 1-minute rain accumulation values reported by the Tempest
Correct, this is the total accumulation between midnight and midnight in the station time zone (i.e. the local day rather than UTC).
This is a post-processed version of (12) after RainCheck has been run. RainCheck is a QC process available for stations in the contiguous US states that attempts to adjust for the uncertainty in the haptic sensor using third-party rain accumulation information. There is more information here: Introducing RainCheck
(20) is the same as (18) except it uses the RainCheck adjusted 1-minute accumulation values (i.e. 19) to calculate the total local day rain accumulation.