Measuring back EMF induced current with multimeter
I don't think you can make any kind of meaningful measurements of short events while using a multimeter. Multimeters react slowly.
The resistance of the coil is of less importance than the impedance.  The impedance depends on the rate of change and the inductance of the coil.  The rate of change will vary as the magnet moves.
Measuring the current as you describe, the current from the coil will be shorted by the ammeter.  You will be measuring the current through the ammeter shunt.  At that moment, the back EMF voltage will be much lower because of the short circuit.  Your calculated voltage based on the resistance of the coil would be wrong because you have to account for the resistance of the ammeter shunt in parallel.

What you can do is to attach a resistor to your coil, then measure the voltage across the resistor while moving the magnet.  The resistor goes to both ends of the coil - it is in parallel to the voltmeter.
From the measured voltage and the known resistance, you can calculate the power dissipated in the resistor and from that you can calculate a current value.
You should use an oscilloscope to measure the voltage.  You can then pick out the peak voltage and determine the peak power, or make an accurate average of the voltage and determine an average power dissipation and average current.
You will find that resistors with different values will give different results.  With some experimentation, you will find a value that will result in the most power dissipation.  That will be at approximately the impedance of your coil.