How can I safely determine the output voltage and current of a transformer?
No. Do not use a Microwave Oven Transformer (MOT) for a Tesla coil.

It is the wrong impedance. The output voltage is too low (around 2kV), spark gaps will not fire reliably. The output current is too high (500mA), if it bites you, you will probably die.

The correct transformer to use is an old style (iron core) Neon Sign Transformer (NST). The output voltage of 15kV is plenty to make very forgiving spark gaps. The output current in the low tens of mA may well be survivable if it bites you.