Let's start from the beginning:
In the definition of Eb/N0 the BW is exactly the one occupied by the signal only (only first harmonic, in you case of square wave). When you will calculate the sensitivity of the overall receiver, then you should also consider the noise in the RX chain filter.
To go in the details of your measurement setup, most probably you are using an 33120A signal generator or a similar one. The only thing that the generator does when switching from 50 ohm load to high impedance load is to double the amplitude of the signal. Just take care of it in your calculation. Be aware of signal reflections when not matched (also if you have only 10 MHz, as you said, there are a lot of harmonics due to square wave shape, and a couple of meter cable can modify the shape of the signal. Check it at both end of cable.
Comments on measurement of bpsk receiver:
there is a 3 dB difference between theory and meas for BER>1e-4. Check Signal level vs. noise level as I said before. Check also the bandwidth of bpsk filter in the receiver. It can add a significant noise if it's BW is larger than modulation BW.
There is a >3dB difference for BER=1e-5 and lower. Maybe you are not taking enough samples in these cases. Be aware that you need to take 10 times samples when going from BER=1e-n to BER=1e-(n+1) to keep the same accuracy.
I hope it can help.
Mazz