1) "No leaving your station without permission" is correct. The other sentence is not correct, and doesn't make sense.
2) You're right that the two sentences in parentheses are not grammatically correct, complete sentences. It's very common to use this style of writing in movie scripts or plays, when you're describing what the actors do. The directions for the actors are rarely written in complete sentences. They simply describe what the actor should do, or what the audience should see or hear.
Sometimes you'll see people use this style even when they're not writing a script. They're using script format to tell a story. It might look something like this:
Joe: "I just called him..." *checks watch* "...ten minutes ago."
Instead of writing the whole sentence "Joe checks his watch," the writer just says "checks watch," but the reader knows that the subject of the action is Joe.