Are freewheels and cassettes interchangeable?
No, freewheels are completely different from the cassette / free hub system and are not interchangeable. 

A freewheel includes the ratchet mechanism that allows the sprockets to rotate backwards as well as the sprockets themselves, and threads into the hub. 

In the cassette / free hub system the ratchet mechanism is built into the hub, and the sprockets slide onto a splined brarrel shaped ‘free hub body’.