This is the first time I've looked at this, so I'm no expert.
The first example is simply wrong so discount it for now.
Here is an article about negation in grammar:
http://en.wikipedia.org/wiki/Affirmative_and_negative
The other two examples either speak negatively or positively: "there was/there was not", "show/do not show". But they both mean essentially the same things until you get down to very small differences.
This is interesting, come back if you still need some help with it and I'll answer you when I have a moment.
The second example:
Don't show fear - don't let people see that you're scared
Show no fear - look very brave
Third:
There *was not* anybody (who could help) - negative - was not
There *was* nobody (who could help) - positive - was
Like I say there are finer levels of meaning, but for now this is all you need to grasp, then go deeper later on.
Keep trying, good luck.