Can an appliance rated for 15A be operated safely on a 20A circuit?

Yes, as long as the circuit is not overloaded. Some kitchen appliances require a dedicated circuit depending on your local code. In my area the following require a dedicated circuit. Dish washer, refrigerator, microwave, garbage disposal, stove, and 2 separate dedicated circuits for all the rest of the kitchen receptacles. Check you local code.

Yes.