I would actually use python for this, but in pure FME I think I would go with an Aggregator (generate list, count attribute) followed by a listHistogrammer.
You can use a ListElementCounter on the list and compare that to the count attribute from the aggregator to get the number of missing attribute
You can use a ListElementCounter on the histogram to get the number of unique values (possibly - 1 if there are null values present and you don't want to count it).
You can use a listSearcher on the histogram to get the null attribute count.
You can sort the histogram by value and the first and last values (ListIndexer) are your min and max. (again excepting the null if present),