Were the prawns raw or cooked before you started? I would cool quickly and reheat if the prawns were raw before you started (ie grey / translucent), but if they were already cooked, and so you have already reheated once, I wouldn't heat again.
You always need to cool rice quickly, and make sure you reheat properly, but treated well, rice is fine. Its if you leave it out you set yourself up for problems.
only if it was cooled quickly and put in the fridge within an hour. Rice harbours a bacteria that produces toxins not destroyed by reheating so if the rice is left at room temperature too long it can cause food poisoning. I'd be a bit wary of feeding it to a young child.