DATE— = — Used to convert a human readable date string (2015/01/01), into a computer readable date string known as Epoch or Unix time. Correct
DATEVALUE— = — Used to convert an Epoch or Unix date/time (computer readable date string) into a human readable date string (2015/01/01). Correct
DATE_IN— = — Used to find dates that fall within a given time period, like day, week, month, quarter, year. Correct
DATE_ADD— = — Used to add or subtract a certain number of units (seconds, minutes, days, etc.) to a given date in order to arrive at a different date. Correct
DATE_CONVERT— = — Used to change the format of one human readable date string (2015/01/01) to another human readable date string (Jan 1, 2015), often for the purposes of sorting. Correct
DATE_STARTOF — = — Returns the first date of a given date period, like week, month, quarter, year.