Plumbing – How to cap off a pipe below by hot water heater’s cutoff valve

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.

You can move the water heater to just about anywhere that would be convenient. However, it is not a good idea to reduce the size down from 3/4" to 1/2" directly off of the tank. You will likely run into issues with water pressure.

In branch plumbing, it is best to keep the size of the pipe at its maximum until it branches off to a specific fixture. Most fixtures, with the exception of a toilet takes 1/2". A toilet is actually reduced to 5/8" by the time it gets to the fill valve. 5/8" is an odd size in plumbing, so most plumbers typically run 1/2" anyway.

You should try to extend the 3/4" pipe as far as you can go, and then tee off of it using multiple 3/4 x 3/4 x 1/2 tees. When you tee off, try to make that run directly to a fixture without teeing off again. This will greatly help keep the water pressure balanced. If all of the plumbing is 1/2", then the fixtures will compete against each other for water because there is not enough volume of water coming through the pipe.