Why 2 electrolytic capacitors and Schottky rectifier at power supply?

DryRun:
3. Why is a high value of 470uF used? I searched and found that many power supply decoupling capacitors are less than 100uF for my application where the supply is only about 12 V DC.

Depends on the rest of the circuit, and the required stability. Very large capacitors are routinely used in combination with bridge rectifiers in power supplies, for example. Well, nowadays most power supplies are switch mode, but 12V power supplies that have a small transformer are still sold as well.