Are "that's it" and "that's all" interchangeable? Is there any specific case where I should use one instead of the other?
That's it is an expression that means:
That's all doesn't seem to be an expression all by itself, but means that there's nothing more to it, that's all you have to do, etc.
So in some cases, as in the second example from the Cambridge Dictionary, they could be used the same way with a slight difference in meaning.
They are more or less interchangeable when they indicate the peremptory end of a discussion. On most other occasions, they are not.