are electrical appliances made in USA compatible in South America, Asia, and Europe?

It depends where. Mostly not, without extra equipment.

Most US appliances need at least around 120V, so you need that voltage supply.

Sometimes they specifically need 60Hz, or work best with 60Hz.

Most of the world uses a nominal 240V 50Hz, so would at least require a transformer to change the voltage. Many heating appliances can use a solid state 240 to 120V converter. Motorized/electronic appliances require an iron transformer, or an active voltage/frequency conversion system.

Generally, your appliance must be pretty special to have to run the 120V 60Hz version in a country with a different supply, and invest in the power conversion, over buying the domestic version where you are.

It depends which parts but all certainly not.