can I use two day old leftover plain rice which had been chilled immedietley and put in airtight containers in the fridge
Yes! Make some fried rice!
Sure! I would use it for several days.
If you make a salad with vinaigrette dressing, you can extend the keeping time.
I often make rice to use a couple of days later for fried rice. To cool it down quickly, I sometimes put it in the fridge spread in a thin layer on a baking sheet with sides - then pile it into an airtight container once it's cold.