That slab looks like Jupiter's atmosphere! Super cool.

Those lines are just natural joints in the stone. They normally form at right angles to the layering. I'm guessing they are smooth and naturally filled with minerals. If not, maybe look a little deeper, but it's not something that strikes me as worrying.

Patagonia is another amazing stone. My, what big minerals you have! In geology-speak, that's called a pegmatite. Definitely not a subtle look!

The rendering suggests you want to use the peninsula for seating. If that is accurate you don’t want a cabinet there. The shelves are a good option, and if your son is together enough to own his own home, I’m sure he can use them appropriately.

I have a 4' square island in my current home. It's fine for 2 folks side by side.

And yes - please get rid of the pantry of despair in the island design. I would rip mine out in a HEARTBEAT.