It’s less than half a quart over. It’s fine.

No just the PCM. Nothing special about the battery.

The car regulates output from the alternator depending on the condition of the battery. If you don’t register the new battery the alternator will overcharge it and reduce the lifespan, thinking it’s still the old battery.

How many miles? The engine uses direct injection, which leads to carbon buildup on the intake valves. Dealerships will sell ‘induction services’ which basically means spraying top-engine cleaner through the intake and taking the car on a spirited drive. If you wait till 60k+ miles then you’ll want to remove the intake and do a proper cleaning of the runners and valves. Spark plugs, air filter and tire pressure also make a difference.