1) The current rating of a gate driver is how much current the driver can drive into the gate. During switching, the gate draws current - the more current you can supply, the faster it will switch. You can think of it like a capacitor - you need to charge it to reach the threshold voltage. The more current you supply, the faster the voltage will increase.
Think of it this way:
simulate this circuit – Schematic created using CircuitLab
The more current the gate driver can supply, the faster "Gate Voltage" will reach the Gate Drive voltage.
2) Yes, but you have to supply the 12V. You must connect it to the
Vs pin. Some gate drivers have internal boost circuitry to create the gate drive voltage, but this one doesn't. You need to create 12V somewhere, and connect it to the
Vs pin so the gate driver can pass it through to the
OUT pins. In the schematic you've drawn you've connected the 12V to the
GND pin. If you connect it to the
Vs pin instead, you'll be on the right track.
3) Yeah sure. The gate driver doesn't really care what is passing through the collector/emitter junction. It's job is just to supply the necessary current and voltage to the gate. If you're happy that it will switch it on and off fast enough, then it is good enough.
Bonus answer, because it would be unethical not to mention it: switching 500V at 5A is not a task for "a new hardware design engineer". That's more than enough to kill you, your customer or an innocent bystander. Please make sure your design is reviewed by someone with more experience before you switch power on.