1. Yes you can plug a refrigerator and a washing machine into the same circuit but this is not recommended because you don't want to trip the breaker and lose power to the fridge.
2. The laundry area still needs a 20 amp circuit run non-stop from the panel to a receptacle meant for the washing machine and connected to nothing else outside the laundry area.
(One morning on WRKO Radio) The tub's not clean! Let's remodel the bathroom.
(One afternoon on WRKO Radio) It's time for an oil change. I'm going to trade in the car for next year's model.