>My question is about the burial depth of 12-2 w/GND cable
Sounds like it will be UF cable hauling 120 V.
18" inches should work.
You also have options of running rigid conduit or pouring concrete over it.

> will conduit be needed where the cabling comes up...?
Yes. Dare I ask what this is running to in your garden?

>Are these subject to local codes?
Yes, if any.

Please protect the circuit with a GFCI before it leaves your house.