Using a CT to measure the current in home electronic devices
The ratio of 50/5A indicates that the transformer will give 5A secondary current with the rated current of 50A through the core and assumes that the secondary is shorted. The 1.5VA rating says that you can take up to 1.5VA of apparent power from the secondary without affecting the accuracy. This corresponds to a voltage of 0.3V across the secondary at 5A.

It sounds like you really need a voltage output proportional to the current which you will get with a higher resistance across the secondary (since the line frequency is constant) but this is not the normal mode of operation. The ratio of secondary voltage to primary current (the transimpedance) depends on the secondary inductance which isn't known but you could measure the output voltage with a range of known primary currents to determine this. If you get too little output, you could wrap the primary cable through the core several times to increase the sensitivity. I doubt that you will get much output with this transformer though since there are too few secondary turns.

You could try experimenting with a 12V toroidal mains transformer, passing one or two turns of your neutral line through the core and loading the original primary (now the secondary) with a resistor of a few k\$\Omega\$. This should give linear results as long as the current is sinusoidal.

And yes, you should pass only one wire through the core.