If your signal was a windowed complex exponential, then the maximum of the magnitude of its discrete-time Fourier transform (DTFT) would equal the frequency of the complex exponential:
The DTFT of $(1)$ is easily computed from the convolution of ...
Your confusion is understandable.
If you consider the definition of linear phase FIR filter and the associated symmetry conditions on their impulse responses, then you can arrive the conclusion that the first two cases
$$ h_1[n] = [0,0,0,1,0] $$
$$ h_2[n] = [0,0,0,0,1,0,0,0,0,0,1] $$
are non-symmetric. However, as you use zeros and ones in those ...
You are missing a couple of zeros.
First of all, you must also include the reciprocal of the one located at $z=-2$, that is one at $z=-0.5$
You should also have one more zero coming from the fact that types 3 and 4 are anti-symmetric. This zero must be located at $z=1$, and is responsible for the minus sign in the anti-mirror image polynomial equation: