OFDM transmitter bandwidth
What should the bandwidth of the BPSK OFDM signal be after resampling?
  Is it 50 Hz (according to theoretical graph shown), 40 Hz (simulated
  before resampling) or 80 Hz?


What you call resampling is actually modelling D/A conversion with a discrete simulation system. Resampling consists of a repetition of every sample plus low pass filtering. Your D/A converter model makes sense but it should not be confused with resampling. The D/A converter can be described by convoluting the discrete time signal with some impulse response $g(t)$. In frequency domain this corresponds to a multiplication of $X(f)$ with $G(f)$ (where these are the Fourier transforms of $x(t), g(t)$). You chose $g(t)$ to be rectangular, so $G(f)$ is a sinc function. As $x$ is a discrete-time signal its frequency spectrum is infinite and so is $G(f)$. The first spectral nulls of $G(f)$ are at $-f_\mathrm{s}$ and $f_\mathrm{s}$. So from your plot it can be seen that a sampling frequency of 40 Hz has been assumed. The useful OFDM signal is in $[-f_\mathrm{s}/2,f_\mathrm{s}/2]$.

So to answer your question: after D/A conversion the spectrum of the OFDM signal is non-zero for arbitrarily high frequencies. To find the 3-dB bandwidth $B$ you have to find the frequency $f_0$ for which $G(f_0)=0.5$, then $B=2f_0$.


  Should a filter be used to achieve the correct bandwidth?


Yes, after D/A conversion, a lowpass filter with cut-off frequency $f_\mathrm{s}/2$ should be used to attenuate the spectral aliases that are caused by the D/A conversion. This so-called reconstruction filter is generally required after D/A conversion and is not OFDM specific. In cases where signal bandwidth doesn't play a role it can be omitted.


  How is OFDM typically implemented to ensure the correct bandwidth; should some subcarriers be set to zero? Should another DAC approach be used?


Typically a lowpass filter with cut-off frequency $f_\mathrm{c} = f_\mathrm{s}/2$ is used. Additionally, some subcarriers at high frequencies are set to zero to enable filtering at $f_\mathrm{c}$ without distorting the useful signal. This is more important at the receiver side where the bandwidth must not exceed $f_\mathrm{s}/2$ in order to avoid aliasing when sampling the received signal. An anti-aliasing lowpass filter is usually applied at the receiver to achieve that.