Since the US Central Pacific HQ on Oahu has a range of 25, and the Solomons are within that range with no enemy units or ZOIs blocking it, it seems I can drop US reinforcements in places like Guadalcanal, Bougainville, Rabaul. Is this correct?
Technically correct but in practice it never happens because the War in Europe value of 0 means Turn 2 units will ALWAYS go to the delayed box. About the only real choice the Allies have of interest is where to place SEAC but since the Commonwealth needs an HQ in India SEAC usually goes to Calcutta.
Secret question I am really asking: did I play the Japanese horribly on Turn 1 and should have had them take Guadalcanal and base an air unit there?
Not at all, notice that the game turn 2 campaign game setup only has Japan with a cruiser and a brigade in Rabaul.