Plumbing – What causes this green residue on pipe going into hot water tank

Carefully dig it out (a garden hose may be useful for "hydro-excavating" right next to the pipe, otherwise some careful trowel and shovel work) and figure out where it does run, then you can decide what to do about it. Beware of possible other poorly buried items while you are digging (wires, etc.)

Assuming you have to work with where it comes out of the garage (Point G) and where it goes into the house(Point H), dig deeper and bury it deeper, reconfiguring the line to fit the deeper trench, and insulating it very well (buried hot water line sounds like cash leaving your wallet in a hurry.) Remove the damaged section of line while you are at it, or change everything between Point G and Point H to PEX.

One relatively good technique for insulating underground lines is to build a box of XPS styrofoam around the pipe and fill that box with polyurethane foam; I'm not sure if you'd have to do anything special to make it termite-resistant, those are not an issue where most people I know are using them to protect heating lines running outside between buildings.

If you would prefer NOT to run it where it runs now, that is certainly an option under "and decide what to do about it" especially if you are up for tearing into the house as much as needed for re-routing the line inside the house.

The pipes behind the furnace look to be part of a heating loop. You should be able to feel that they cool off and then get hotter again when the thermostat calls for heat. Your hot water heater has a vent, so I assume it is gas fired, and wouldn't be connected to the furnace.