Multi-class classification configuration
In my experience the activations are irrelevant to whether the classes are binary or multi-class. Their effectiveness depends on the kind of data you have. 

Furthermore, there is one node in the layer because you are doing a binary classification. In other words, when the value of the last node is low or below a threshold the class is 0 and 1 if otherwise(value of last node is high or above a thresold).

And yes, if there are more classes you need as many nodes in the last Dense Layer. You can also you 2 nodes when you only have two classes in your data and predicting the one with the highest score/output.