The 1N400X series are all 1A diodes and are upwards compatible.

Meaning if the unit has a 1N4002 or a 1N4004 in it anything HIGHER is fine IE: 1N4007

I don't even bother stocking anything other than 1N4007 any more. In the olden days there was a significant price difference between them but not any more.

I would certainly fit a diode to EVERY coil confirming the banded end is installed facing the +ve power feed to the coil. I would say there are very few (if any) situations where a diode should NOT be installed.

Even in games where the diode is actually installed on the PCB itself I would still fit a diode to the coil - it can't do any harm at all and is good insurance. It also prevents spurious spikes from running all through the wiring harness.