Hi walterc,
Regarding the MOSFET, the max output current is related to the gate drive, as shown in Figure 2 of the datasheet:
Looking at the graph, it limits out at about 30A at 4.5V, 42A at 5V, etc. The higher the Vgs (to a point) the lower the Rds-on, which is the limiting factor in how much current it can carry. Basically, getting it up to it’s full capability means applying 8V or more.
I would note that the IRF3415 is a relatively old MOSFET, and that some of the newer ones will have improved characteristics. Since your application does not require fast switching (it’s not a PWM application), focusing on parts with a very low Rds-on will minimize heat production.
Parts like the IPP026N10NF2SAKMA1 or IPP019N08NF2SAKMA1 are decent compromises of Rds-on, voltage rating, availability, and pricing.
The 7800 series of regulators should work fine for generating your gate voltage. Some other LDO type regulators have a minimum load current requirement which might be unsuitable for this application, but the 7800 series does not have this issue.
That pull-down resistor is fairly important because it ensures that the MOSFET gate is pulled low when the input is off. Otherwise internal capacitance in the MOSFET may maintain a voltage on the gate even when the optoisolator is off. This could keep the MOSFET partially turned on, which is obviously undesirable.
Yes, 500mA is more than enough. Without the requirement for high-speed switching (you’re not doing PWM), even a few tens of milliamps would likely be sufficient. The only time the gate draws significant current is the first few microseconds as the input capacitance of the FET gets charged. After that it draws essentially zero current.
There really aren’t any “high current” breadboards, as far as I am aware of. If you get your MOSFET properly turned on, it should not be a significant source of heat, so that shouldn’t be an issue. Regarding the current, 6A steady-state isn’t extremely high, so that may not be a real problem. To minimise that risk, I’d either plug multiple wires from the motor to the nearest possible holes to the MOSFET Drain and place several wires from the ground bus to adjacent holes of the Source. Better yet, use external jumpers and clip directly to the legs of the MOSFET.