Use Current Sensing Transformer Instead of Power Transformer

In a perfect transformer run in forward mode, the change in secondary current exactly ballances the change in primary current to keep the magnetic flux the same.

This means the effective current going around the core in each of the primary and secondary must be the same but in opposite direction. The transformer only sees the current going around the core. The multiple turns of a winding only make it look like more current overall going around. To the core, 13 turns of 1 A each is the same as 26 turns at 1/2 A each. The same overall current is still circling the core.

The current that actually flows thru each winding from the external circuit point of view is the current thru each winding since they are effectively in series. The external current is therefore inversely proportional to the number of windings.

Let's say your transformer has 100 A circling the core. That might be 880 turns on the primary, for 114 mA thru the primary from the outside point of view. In this case, the secondary would have only 44 turns. For the ideal case, this would also have to produce 100 A circling the core. Since each turn only contributes 1/40 of that, the current thru the secondary wire needs to be 2.5 A.

1. The voltage spike is caused by the secondary coil not having a discharge path: Inductors oppose change in current flowing through them. Disconnecting the coil forces the current flow to stop instantly. Thus the inductor must find a path to discharge the energy stored in it, and unless it finds such a path, the behavior is of voltage across the coil rising to an arbitrary level. This mechanism is very effectively used in a variety of designs requiring very high voltages, such as some automotive ignition coils and other such devices.
2. Keep the load resistor in place. Disconnect the sensing connection alone.
3. In the secondary.
4. Yes, the burden or load resistor is designed to provide a current path, with the voltage read across it. The sensing device's impedance appears in parallel to the burden resistor, splitting the coil current. If the sensing equipment is high impedance, e.g. a solid state multimeter as opposed to a low-impedance vintage coil voltmeter, this parallel load is insignificant.
5. No.