Q&A for How to Test a Ground Rod

No, you would generally need to run the equipment grounding conductor (EGC) in the same cable as the line and neutral conductors that supply the transformer in its new location, terminating all three conductors inside a junction box. The EGC wire would then attach to the transformer's wire as well as the junction box, if the box is metal. You could also use properly installed metallic conduit as the EGC path to ground.

In NEC (2014): 250.53(A)(3) and 250.53(B) seem to say additional electrode rods shall "not be less than 1.83 m (6 feet) apart". However, it is noted that the "paralleling efficiency is increased by spacing them twice the length of the longest rod."

Yes, the grounded slot in electrical outlets is "live" in the sense that it is intended to conduct the power used by devices plugged into it, same as the "hot" slot. It also happens to be grounded at the service panel, if done properly, as is the grounding slot in a three-slot receptacle. The grounding conductor is, however, intended for safety from electrocution, not to carry any significant power during normal use.

The grounding conductors need to be "protected from physical damage", typically in a rigid conduit of some kind. See, e.g., NEC (2014): 250.64. Laying them "on top of the grass" risks breaking them when someone places equipment on top of the unprotected conductor or snagging it with yard equipment or when simply walking by.

Rods or other grounding electrodes that are closer than 6 feet do not meet "code" in many places, and provide substantially reduced grounding efficiency.

Most portable generators do not need to be grounded, where everything plugs into its receptacles and the frame provides the necessary "grounding" for use of those appliances. However, if it's connected to circuits in your home, then it must be grounded. Yes, the 8-ft rod (or acceptable equivalent electrode) would be required.