# The Nyquist-Theorm behind the fft

I saw a code in Python in the scipy.org (http://docs.scipy.org/doc/scipy-dev/reference/tutorial/fftpack.html) and found this:

First question: Is it right that T = 1/800 <==> fs = 800 Hz fulfill the condition fs = 2*fmax, because the maximum frequency of the funtion contains 80 Hz?
Second question is in the row: xf = np.linspace(0.0,1.0/(2.0*T), N/2):
I have often seen that people use the nyquist freqency in the x-axis for the the freqencies spectrum why is that so?
And if I ignore the (1/2 * 1/T) and N/2 and write in my code for xf = np.linspace(0.0, 1.0/T, N) instead of np.linspace(0.0, 1.0/(2.0*T), N/2) so I get a graph like this

Why do I get here a mirroring at the 400 Hz? Does it something to do with the symmetries of the fft?
I appreiate it if someone can help me to explain my question, thx alot!