Water coming in BELOW sump pit inlet pipe! Is this normal?
Apart from routing a sump pump for water around a foundation to a sanitary drain (no storm sewers where you live?), this sounds normal.

Usually, the perforated piping is just a supplement to the classic French drain design using rocks. The pipe is to ensure there is always a path with low resistance when the water table gets high enough. Otherwise, some water should still find its way through the rocks/soil when the water table is above the sump pit basin and below the bottom of the pipe.