How does the number of frequency-domain sampling points influence the outcome of an inverse FFT?
Regarding example 1:
first of all, either the fft or the ifft needs to be normalised by the number of sampling points as you have done (actually you can normalise each by a factor of the square root of the number of points, it is just a meter of definition). However, in your case the ifft is half the length of the fft you performed. Hence your signal is divided by 2. If you would perform the normalisation when calling the ifft (using half the original number of samples) you should get the correct height.
Now, regrading the second part of the signal, it is not truncated. What you see is some kind of aliasing. Since you downsampled  without filtering, you get aliasing. This is the same concept as frequency aliasing (DFT and IDFT are basically the same). You should try to flip the input signal in the time domain and witness the results.  

Next, regarding example 2:
Your problem is with the number of sampling points. Let me start by mentioning that since your signal is real, the frequency domain is symmetric.
In your first example you had even number of points. when you downsampled the frequency you still got a symmetric signal. In the second example you have odd number of samples. Therefore your decimated frequencies are not symmetric and the result is a complex signal. If you try it with one less (or more) sample it should give a similar result to example 1. On the other hand you can perform the frequency decimation while keeping the signal symmetric.