Can DC devices run on AC?

AC devices like your washing machine, dishwasher, refrigerator and fans can't work off DC. Your air conditioning maybe can if the description includes the word "inverter", otherwise no. These devices typically run on mains-connected AC motors. Wrong voltage or frequency, and they won't work.

Moreover, what happens if you run a DC motor on AC power?

When A.C. supply is given to a D.C. motor: 1)In case of Series connection of armature winding and field winding , it may run. 2)But, In case of parallel connection , it won't rotate at all and will start humming and will create vibrations, as a torque produced by positive and negative cycle will cancel out each other.