Is it normal to feel a child's (age 5) pulse directly over heart on chest? he's had diarrhea but no fever. pulse seems hard and fast.

It is normal to be: able to feel the heartbeat there, but will be more obvious with a faster heart rate. Illness can increase the heart rate in general, as can fever and also dehydration. Is he having a lot of diarrhea? Is he urinating less than usual? If so, he may be dehydrated. I would recommend you call his pediatrician to discuss and possibly have him examined.

Yes: Until they develop the muscle mass of adolescence it is relatively easy to feel the heartbeat over the chest.