Yes, this rod is correct, only it is NOT "additional", it is required since this feeder runs to a detached structure.
Also, as mentioned, many/most inspectors will as if the ground rod meet the 25 ohm requirement. If it does not then a second rod is required and the 25 ohm rule is no longer in place.
Also, and this is a biggie, that SOOW cord is absolutely NOT code legal in this case. Rubber cord CANNOT be used for permanent wiring. You need to use either individual THHN/THWN conductors if the conduit is complete from panel to panel, or you can use UF cable as long as the size cable you get can legally fit in the conduit.
Individual conductors in conduit could be #8cu, but due to the distance and the small cost difference I'd go with #6, actually #6 for the hots, #8 for the neutral, and #10 for the ground.
Uf cable would need to be 6/3.
I would seriously consider making this right and getting the whole job inspected.
I'm fine with the idea of a main panel with only 2 things in it feeding a sub-panel with everything in it.
Question #1 - I'd rethink putting a service panel outdoors at all. Weather is rough on panels, even if they claim to be outdoor rated. I'm a little nervous about a 100A breaker supplied from the normal bus bars, but if the manufacturer stands behind it, okay. The 100A wires are going to be a mother to wrestle onto that 100A breaker. Are you quite sure the power company has provisioned you 125A service? 100A is more common.
Question #1 (the second): You're gonna want more slots than 24, since this box powers pretty much your whole house. Nobody ever installed an addition and went "Gosh, that job was sure made harder and more expensive by having too many slots in the panel". It's a false economy, especially since bigger boxes are often bundled with more breakers. Your house may be ok now, but do a kitchen remodel and lookout!
Question #2 (the second): Don't bond your grounds to random plumbing that happens to be going by. It's not code, and someday you might have a plumbing problem and the plumber replaces a downstream chunk of it with PVC. Whoops. Also, they've been upgrading customers to PLASTIC water meters. Double whoops. Bond properly and to code.
Question #3 (the third): Bond ground and neutral only in the (singular) main panel. As such, you need 4 wires between main and subpanel.
Just for your edification, it's only a sub-panel if it's fed from a main panel. If it's fed directly from a transformer, it's a main panel.
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