(1) Does NEC allow a single 120V ckt to be run to an exterior tool/storage shed via GFCI control, having only a Simple Disconnect in the tool/storage shed? NEC cites? (2) Using UF cable, What is the depth requirement?
If the GFCI protection is on the line side of the excavation at a 1&2 family dwelling the answer is 12" depth 300.5. The exception to 250.32(A) allows you to skip the ground electrode system for a single circuit but 225.31 does not give you relief on the disconnect.
I hate to say this, but you were in violation of the NEC the moment you asked the question.
Why? Because the NEC, as detailed in Article, is NOT a design manual. The moment you try to 'design to code,' you're off to a bad start.
Apart from that, there are other considerations.
For example, the depth you bury the cable is influenced by what use the ground over the cable gets, and what else is there to protect the cable. You're not doing yourself any favors if the cable is damaged every time the gardener works on the lawn sprinkler system. In a nutshell, "Deeper is better."
Likewise, good practice might suggest a 'handhole' or junction box at either end of the run. This will help you avoid having tom open walls later if you need to replace the cable. (Maybe I should make that "WHEN" you need to replace the cable). The junction boxes also make it easier to identify exactly where the cable lies. There's no 'law' that says you must do this, but it might be a smart thing to do.
Then there's the matter of Murphy's law. One light becomes a light and a receptacle, then a workbench full of power tools, then you want heat ... before you know it, you're out there digging again. I don't know about you, but I hate digging - and customers don't like the scar left over the trench. So, I really like to run wires in pipe, rather than UF cable. Bury the pipe deep, so the roto-tiller doesn't hit it. Since PVC pipe is cheap, there's no reason to run anything smaller than 1". There's then plenty of room for future additions.
Trench depth is something frequently modified by local ordinance. For example, in my very, very rocky area the city still wants everything buried 24".
Finally, even though listed means of splicing direct-buried cable exist, my experience suggests that you really, really want a handhole for your splices. If nothing else, this gives you an access point for future troubleshooting.