1) What's the shortest term for this concept?
"not disclosing information ORALLY"
"not disclosing oral information".
I mean something like this: "protection of oral information" or...
2) "Counterespionage" are the things to do for detecting and preventing "espionage". Now what are the things to do for detecting and preventing "overthrow"?
The context for your first question is not clear, but I can imagine that the first sentence is more appropriate (it means that you can't share information by talking about it, but perhaps in written form) However, without context, I really can't be sure.
#2 could be "counter revolution" but again, your request isn't completely clear!
Hope that helps