Since you posted this question in the "Alerts and Notifications" topic of the forum the solution I provide can be used as a Study Alert or as a custom scan. This does not work as a chart study, but considerable modifications can adapt this code to a chart study.
The following solution performs according to the 4 bullet points I added to the question after getting clarifications on the missing details of this request. The alert will trigger once all the conditions have been satisfied and the bar closes (the next bar opens).
input maLengthOne = 20;
input maTypeOne = AverageType.EXPONENTIAL;
input maPriceOne = close;
def maOne = MovingAverage(maTypeOne, maPriceOne, maLengthOne);
def priceCrossBelowAverage = close[1] > maOne[1] and close < maOne;
def triggerAlert = priceCrossBelowAverage[1] and low < low[1] and close < maOne;
plot signal = triggerAlert[1];