After ne...pas, is des ever used ?

Yes, after être or other verbes d'état (there's a link to the full list in the lesson).

For example:

"Ce ne sont pas des choses aisées à dire" - "these are not easy things to say"

 

Except for être and other verbs of state, is des used after ne ... pas ?  

It's also used in some figurative expressions:

"ça ne casse pas des briques"

"les chiens ne font pas des chats"

I'm not sure why "de" is not used in these examples.