It's been our practice to analyze the table/index partition as well as the global table/indicies as soon as the partitions are added. So the stats are always zero for those partitions. In the past we have hardly ever analyzed the partitions or global tables/indicies after the partitions are loaded with data - I know we probably should, but since we don't get any complaints of performance, we stick by the "if it ain't broke ..." rule !

Is the table analyzed as a whole, as well as the individual partitions?
Yes, the query does have the partition key in the where clause.